Download App

Derivatives — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDerivatives4 Marks
Question
Differentiate the following from first principle:$\text{x}^3+4\text{x}^2+3\text{x}+2$
✓

Answer

We have,$\text{f(x)}=\text{x}^3+4\text{x}^2+3\text{x}+2$
$\because\text{f}'\text{(x)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}(\text{x+h})-\text{f}(\text{x})}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{(\text{x+h})^3+4(\text{x+h})^2+3(\text{x+h})+2-(\text{x}^3+4\text{x}^2+3\text{x}+2)}{\text{h}}$
On solving we get,$=\lim\limits_{\text{h}\rightarrow0}\frac{\text{x}^3+\text{h}^3+3\text{x}^2\text{h}+3\text{h}^2\text{x}+4\text{x}^2+4\text{h}^2+8\text{hx}+3\text{x}+3\text{h}+2-\text{x}^3-4\text{x}^2-3\text{x}-2}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{3\text{x}^2\text{h}+3\text{xh}^2+\text{h}^3+4\text{h}^2+8\text{hx}+3\text{h}}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}3\text{x}^2+3\text{xh}+\text{h}^2+4\text{h}+8\text{x}+3$
$=3\text{x}^2+8\text{x}+3$

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.(4 Marks)" from Derivatives→Derivatives — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Convert the complex numbers in polar form and also in exponential form.

$z=\frac{2+6 \sqrt{3} i}{5+\sqrt{3} i}$

→
Find the equation of the tangent to the hyperbola.: $\frac{x^2}{16}-\frac{y^2}{9}=1$ at the point in a first quadrant whose ordinate is 3.
→
If a, b, c are in A.P. b, c, d are in G.P. and $\frac{1}{\text{c}},\frac{1}{\text{d}},\frac{1}{\text{e}}$ are in A.P., prove that a, c, e are in G.P.
→
Express the following complex numbers in polar form and exponential form.

$\frac{1+7 i }{(2- i )^2}$

→
Show that the line $8 y+x=17$ touches the ellipse $x^2+4 y^2=17$. Find the point of contact.
→
Prove that the tetrahedron with vertices at the points O(0, 0, 0), A(0, 1, 1), B(1, 0, 1) and C(1, 1, 0) is a regular one.
→
Prove that:
$\cos3\text{A}+\cos5\text{A}+\cos7\text{A}+\cos15\text{A}=4\cos4\text{A}\cos5\text{A}\cos6\text{A}$
→
The perpendicular distance of a line from the origin is 5 units and its slope is -1. Find the equation of the line.
→
Differentiate the following functions with respect to x:$\frac{\sin\text{x}-\text{x}\cos\text{x}}{\text{x}\sin\text{x}+\cos\text{x}}$
→
Sketch the graphs of the following trigonometric functions:
$\text{u(x)}=\cos^2\frac{\text{x}}{2}$
→