Differentiate the following functions with respect to x: (e^ ) - Vidyadip

Question

Differentiate the following functions with respect to x:
$\tan(\text{e}^{\sin\text{x}})$

✓

Answer

Consider $\text{y}=\tan(\text{e}^{\sin\text{x}})$
Differentiate with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\big[\tan\text{e}^{\sin\text{x}}\big]$
$=\sec^2\big(\text{e}^{\sin\text{e}}\big)\frac{\text{d}}{\text{dx}}\big(\text{e}^{\sin\text{x}}\big)$
[Using chain rule]
$=\sec^2\big(\text{e}^{\sin\text{x}}\big)\times\text{e}^{\sin\text{x}}\times\frac{\text{d}}{\text{dx}}(\sin\text{ x})$

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 "3 Marks Question" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\frac{1}{\text{x}^{\frac{3}{2}}}\text{dx}$

Evaluate:$\int \frac{1 + x^{2}}{1 + x^{4}} \text{dx}$

Write a value of $\int\text{e}^{\text{x}}\sec\text{x}(1+\tan\text{x})\text{dx}$

Find the area of the parallelogram whose adjacent sides are determined by the vectors $\vec{a}=\hat{i}-\hat{j}+3 \hat{k}$ and $\vec{b}=2 \hat{i}-7 \hat{j}+\hat{k}$.

Differentiate the following functions with respect to x:
$\tan^2\text{x}$

Integrate the function $\frac{1}{\sqrt{(2-x)^{2}+1}}$

If $\text{x}=\text{a}(\theta-\sin\theta)\text{ and},\text{y}=\text{a}(1+\cos\theta),$ find $\frac{\text{dy}}{\text{dx}}\text{ at }\theta=\frac{\pi}{3}$

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\log\tan\text{x dx}$

The probability is 0.02 that an item produced by a factory is defective. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.

Write a value of $\int\tan^6\text{x}\sec^2\text{x}\text{ dx}$