Download App

Differentiation (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Differentiation (p-1)2 Marks
Question
Differentiate the following w.r.t. x. : $\sqrt{x}\left(x^2+1\right)^2$
✓

Answer

$
\text { Let } \begin{aligned}
\mathrm{y} & =\sqrt{x}\left(x^2+1\right)^2 \\
y & =x^{\frac{1}{2}}\left(x^4+2 x^2+1\right) \\
y & =x^{\frac{9}{2}}+2 x^{\frac{5}{2}}+x^{\frac{1}{2}}
\end{aligned}
$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{\mathrm{d}}{\mathrm{d} x}\left(x^{\frac{9}{2}}+2 x^{\frac{5}{2}}+x^{\frac{1}{2}}\right) \\
& =\frac{\mathrm{d}}{\mathrm{d} x} x^{\frac{9}{2}}+2 \frac{\mathrm{d}}{\mathrm{d} x} x^{\frac{5}{2}}+\frac{\mathrm{d}}{\mathrm{d} x} \sqrt{x} \\
& =\frac{9}{2} x^{\frac{9}{2}-1}+2 \times \frac{5}{2} x^{\frac{5}{2}-1}+\frac{1}{2 \sqrt{x}} \\
& =\frac{9}{2} x^{\frac{7}{2}}+5 x^{\frac{3}{2}}+\frac{1}{2 \sqrt{x}}
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Differentiation (p-1)→Differentiation (p-1) — all question types→Maths (commerce) STD 11 Commerce / Arts question papers→Maharashtra Board STD 11 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Find $\mathrm{n}$ if ${ }^{21} \mathrm{C}_{6 \mathrm{n}}={ }^{21} C_{n^2+5}$
→
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
→
Find $\frac{d y}{d x}$ if : $\mathrm{y}=\frac{(\log x+1)}{x}$
→
Four cards are drawn from a pack of 52 cards. Find the probability that: 3 are Kings and 1 is Jack.
→
Find the value of k for which the points P(k, -1), Q(2, 1) and R(4, 5) are collinear.
→
If $A(4,1)$ and $B(5,4)$, find the equation of the locus of point $P$ if $P A^2=3 P B^2$.
→
The mean and variance of a distribution are 60 and 100 respectively. Find the mode and the median of the distribution if $S k_p=-0.3$.
→
M/s Janaseva sweet mart sold sweets of $₹ 3,86,000$. What CGST and SGST he will pay if the rate of GST is $5 \%$ ?
→
A function f is defined as follows:
f(x) = 4x + 5, for -4 ≤ x < 0. Find the values of f(-1), f(-2), f(0), if they exist.
→
Thane is the 20th station from C.S.T. If a passenger can purchase a ticket from any station to any other station, how many different tickets must be available at the booking window?
→