Download App

Derivatives — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDerivatives3 Marks
Question
Differentiate the following from first principle:$\text{e}^{\text{3x}}$
✓

Answer

We have, $\text{f(x)}=\text{e}^{3\text{x}}$ $\because\text{f}'\text{(x)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}\big(\text{x+h}\big)-\text{f}\big(\text{x}\big)}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{e}^{3\text{(x+h)}}-\text{e}^{3\text{x}}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{e}^{3\text{(x)}}.\text{e}^{3\text{h}}-\text{e}^{3\text{x}}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{e}^{3\text{(x)}}(\text{e}^{3\text{h}}-1)}{\text{h}}$Multiplying Numerator and Denominator by 3
$=\lim\limits_{\text{h}\rightarrow0}\text{e}^{3\text{(x)}}\frac{(\text{e}^{3\text{h}}-1)}{3\text{h}}$ $\bigg[=\lim\limits_{\text{h}\rightarrow0}\frac{\text{e}^{3\text{h}}-1}{3}=1\bigg]$ $=3\text{e}^{3\text{x}}$

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.(3 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

Find the equation of the hyperbola referred to its principal axes: whose distance between directrices is $\frac{8}{3}$ and eccentricity is $\frac{3}{2}$.
→
Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to a line having slope $\frac{1}{2}.$
→
Show that : $\sec 840^{\circ} \cdot \cot \left(-945^{\circ}\right)+\sin 600^{\circ} \cdot \tan \left(-690^{\circ}\right) \ =\frac{3}{2}$
→
If $f(x) = x^2$, find $\frac{\text{f}(1.1)-\text{f}(1)}{(1.1)-1}$
→
Find the general solutions of the following equations:
$\sin\text{x}=\tan\text{x}$
→
Find the differences between the greatest values in the following:

${ }^{15} C_r$ and ${ }^{11} C_r$

→
Find the equation of the circle passing through the points:
$(5, -8), (-2, 9)$ and $(2, 1)$
→
In the following expansions, find the indicated coefficients.

$x^{-20}$ in $\left(x^3-\frac{1}{2 x^2}\right)^{15}$

→
The arithmetic mean of runs scored by 3 batsmen Varad, Viraj and Akhilesh in the same series are 50, 52 and 21 respectively. The standard deviation of their runs are 11, 16 and 5 respectively. Who is the most consistent of the three? If one of the three is to be selected, who will be selected?
→
How many terms of the G.P. $3,\frac{3}{2},\frac{3}{4},\ \dots$ be taken together to make $\frac{3069}{512}?$
→