Download App

Maths Solve the Following Question.(2 Marks)

Differentiation · Maharashtra Board STD 11 Science (MSBSHSE - English Medium). 16 questions.

Questions

Solve the Following Question.(2 Marks)

Take a timed test

16 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
If $y =\frac{ e ^x}{\sqrt{x}}$, find $\frac{d y}{d x}$ when $x =1$
Answer
$
y=\frac{ e ^x}{\sqrt{x}}
$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(\frac{ e ^x}{\sqrt{x}}\right) \\
& =\frac{\sqrt{x} \frac{ d }{ d x} e ^x- e ^x \frac{ d }{ d x} \sqrt{x}}{(\sqrt{x})^2} \\
& =\frac{\sqrt{x} e ^x- e ^x \frac{1}{2 \sqrt{x}}}{x} \\
\frac{ d y}{ d x} & =\frac{2 x \cdot e ^x- e ^x}{2 \sqrt{x} x}
\end{aligned}
$
When $x=1$,
$
\frac{ d y}{ d x}=\frac{2(1) e ^1- e ^{ l }}{2 \sqrt{1} .1}=\frac{2 e - e }{2}=\frac{ e }{2}
$
View full question & answer→
Question 22 Marks
Differentiate the following w.r.t. x :  $y=\frac{5 e^x-4}{3 e^x-2}$
Answer
$
y=\frac{5 e ^x-4}{3 e ^x-2}
$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
& \frac{ d y}{ d x}=\frac{ d }{ d x}\left(\frac{5 e ^x-4}{3 e ^x-2}\right) \\
= & \frac{\left(3 e ^x-2\right) \frac{ d }{ d x}\left(5 e ^x-4\right)-\left(5 e ^x-4\right) \frac{ d }{ d x}\left(3 e ^x-2\right)}{\left(3 e ^x-2\right)^2} \\
= & \frac{\left(3 e ^x-2\right)\left(5 \frac{ d }{ d x} e ^x-\frac{ d }{ d x} 4\right)-\left(5 e ^x-4\right)\left(3 \frac{ d }{ d x} e ^x-\frac{ d }{ d x} 2\right)}{\left(3 e ^x-2\right)^2} \\
= & \frac{\left(3 e ^x-2\right)\left(5 e ^x-0\right)-\left(5 e ^x-4\right)\left(3 e ^x-0\right)}{\left(3 e ^x-2\right)^2} \\
= & \frac{15\left( e ^x\right)^2-10 e ^x-15\left( e ^x\right)^2+12 e ^x}{\left(3 e ^x-2\right)^2}=\frac{2 e ^x}{\left(3 e ^x-2\right)^2}
\end{aligned}
$
View full question & answer→
Question 32 Marks
Differentiate the following w.r.t. x : $y=\frac{x^2+3}{x^2-5}$
Answer
$y=\frac{x^2+3}{x^2-5}$
Differentiating w.r.t. $x$, we get
$\begin{aligned}
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(\frac{x^2+3}{x^2-5}\right) \\
& =\frac{\left(x^2-5\right) \frac{ d }{ d x}\left(x^2+3\right)-\left(x^2+3\right) \frac{ d }{ d x}\left(x^2-5\right)}{\left(x^2-5\right)^2} \\
& =\frac{\left(x^2-5\right)(2 x)-\left(x^2+3\right)(2 x)}{\left(x^2-5\right)^2} \\
& =\frac{2 x\left(x^2-5-x^2-3\right)}{\left(x^2-5\right)^2} \\
& =\frac{2 x(-8)}{\left(x^2-5\right)^2}=\frac{-16 x}{\left(x^2-5\right)^2}
\end{aligned}$
View full question & answer→
Question 102 Marks
Differentiate the following w.r.t. x :
$y=3 \cot x-5 e^x+3 \log x-\frac{4}{x^{\frac{3}{4}}}$
Answer
$y=3 \cot x-5 e ^x+3 \log x-\frac{4}{x^{\frac{3}{4}}}$
Differentiating w.r.t. $x$, we get
$\frac{ d y}{ d x}=\frac{ d }{ d x}\left(3 \cot x-5 e ^x+3 \log x-\frac{4}{x^{\frac{3}{4}}}\right)$
$\frac{ d y}{ d x}=3 \frac{ d }{ d x}(\cot x)-5 \frac{ d }{ d x}\left( e ^x\right)+3 \frac{ d }{ d x}(\log x)$
$-4 \frac{ d }{ dx }\left(x^{-\frac{3}{4}}\right)$
$=3\left(-\operatorname{cosec}^2 x\right)-5 e ^x+3\left(\frac{1}{x}\right)-4\left(-\frac{3}{4} x^{-\frac{3}{4}-1}\right)$
$=-3 \operatorname{cosec}^2 x-5 e ^x+\frac{3}{x}+3 x^{\frac{-7}{4}}$
$=-3 \operatorname{cosec}^2 x-5 e ^x+\frac{3}{x}+\frac{3}{x^{\frac{7}{4}}}$
View full question & answer→
Question 112 Marks
Differentiate the following w.r.t. x :

$y=7^x+x^7-\frac{2}{3} x \sqrt{x}-\log x+7^7$

Answer
$y=7^x+x^7-\frac{2}{3} x \sqrt{x}-\log x+7^7$
Differentiating w.r.t. $x$, we get
$\begin{aligned}
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(7^x+x^7-\frac{2}{3} x \sqrt{x}-\log x+7^7\right) \\
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(7^x\right)+\frac{ d }{ d x}\left(x^7\right)-\frac{2}{3} \cdot \frac{ d }{ d x}\left(x^{\frac{3}{2}}\right)-\frac{ d }{ d x}(\log x)+\frac{ d }{ d x}\left(7^7\right) \\
& =7^x \log 7+7 x^6-\frac{2}{3} \times \frac{3}{2} x^{\frac{3}{2}-1}-\frac{1}{x}+0 \\
& =7^x \log 7+7 x^6-x^{\frac{1}{2}}-\frac{1}{x} \\
& =7^x \log 7+7 x^6-\sqrt{x}-\frac{1}{x}
\end{aligned}$
View full question & answer→
Question 122 Marks
Differentiate the following w.r.t. x :
$y=x^{\frac{7}{3}}+5 x^{\frac{4}{5}}-\frac{5}{x^{\frac{2}{5}}}$
Answer
$y=x^{\frac{7}{3}}+5 x^{\frac{4}{5}}-\frac{5}{x^{\frac{2}{5}}}$
Differentiating w.r.t. $x$, we get
$ \frac{ d y}{ d x}=\frac{ d }{ d x}\left(x^{\frac{7}{3}}+5 x^{\frac{4}{5}}-\frac{5}{x^{\frac{2}{5}}}\right)$
$\frac{ d y}{ d x}=\frac{ d }{ d x}\left(x^{\frac{7}{3}}\right)+5 \frac{ d }{ d x}\left(x^{\frac{4}{5}}\right)-5 \frac{ d }{ d x}\left(x^{-\frac{2}{5}}\right) $
$ =\frac{7}{3} x^{\frac{7}{3}-1}+5\left(\frac{4}{5} x^{\frac{4}{5}-1}\right)-5\left(-\frac{2}{5} x^{-\frac{2}{5}-1}\right)$
$=\frac{7}{3} x^{\frac{4}{3}}+4 x^{\frac{-1}{5}}+2 x^{\frac{-7}{5}}$
$=\frac{7}{3} x^{\frac{4}{3}}+\frac{4}{x^{\frac{1}{5}}}+\frac{2}{x^{\frac{7}{5}}} $
View full question & answer→
Question 132 Marks
Differentiate the following w.r.t. x :
$y=\log x-\operatorname{cosec} x+5^x-\frac{3}{x^{\frac{3}{2}}}$
Answer
$y=\log x-\operatorname{cosec} x+5^x-\frac{3}{x^{\frac{3}{2}}}$
Differentiating w.r.t. $x$, we get
$\frac{d y}{d x}=\frac{d}{d x}\left(\log x-\operatorname{cosec} x+5^x-\frac{3}{x^{\frac{3}{2}}}\right)$
$\frac{d y}{d x}=\frac{d}{d x}(\log x)-\frac{d}{d x}(\operatorname{cosec} x)+\frac{d}{d x}\left(5^x\right)$
$-3 \frac{d}{d x}\left(x^{-\frac{3}{2}}\right)$
$=\frac{1}{x}-(-\operatorname{cosec} x \cot x)+5^x \log 5$
$-3\left(-\frac{3}{2} x^{\frac{-3}{2}-1}\right)$
$=\frac{1}{x}-(-\operatorname{cosec} x \cot x)+5^x \log 5$
$-3\left(-\frac{3}{2} x^{\frac{-5}{2}}\right)$
$=\frac{1}{x}+\operatorname{cosec} x \cot x+5^x \log 5+\frac{9}{2 x^{\frac{5}{2}}}$
View full question & answer→
Question 152 Marks
Find the derivatives of the following w.r.t. $x$ by using the method of the first principle.
$e^{2x+1}$
View full question & answer→
Question 162 Marks
Find the derivatives of the following w.r.t. $x$ by using the method of the first principle.
$x^2 + 3x – 1$
View full question & answer→
Generate Paper FreeAll Differentiation topics