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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Prove the following:
$\tan^{-1}\Bigg(\frac{1}{3}\Bigg)+\tan^{-1}\Bigg(\frac{1}{5}\Bigg)+\tan^{-1}\Bigg(\frac{1}{7}\Bigg)+\tan^{-1}\Bigg(\frac{1}{8}\Bigg)=\frac{\pi}{4}.$

Write the value of $\sin^{-1}\Big(\frac{-\sqrt3}{2}\Big)+\cos^{-1}\Big(\frac{-1}{2}\Big)$

Let f, g, h be real functions given by f(x) = sinx, g(x) = 2x and h(x) = cosx. Prove that fog = go(fh).

Differentiate the following functions from first principles:
$e^{3x}$.

By using the properties of definite integral, evaluate the integral in Exercise:
$\int\limits_{2}^{8}|\text{x}-5|\ \text{dx}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal.
$(0.0037)^{\frac{1}{2}}$

Evaluate the following definite integrals:
$\int_{0}^\limits{\frac{\pi}{2}}\cos^2\text{x}\text{ dx}$

Find the shortest distance between the lines whose vector equations are $\vec r = \hat i + 2\hat j + 3\hat k$ + $\lambda \left( {\hat i - 3\hat j + 2\hat k} \right)$ and $\vec r = 4\hat i + 5\hat j + 6\hat k$ + $\mu \left( {2\hat i + 3\hat j + \hat k} \right)$

Using properties of determinants, prove the following:
$\begin{vmatrix}\text{a}+\text{b}+\text{c} & -\text{c} & -\text{b} \\-\text{c} & \text{a}+\text{b}+\text{c} & -\text{a}\\-\text{b} & -\text{a} & \text{a}+\text{b}+\text{c} \end{vmatrix}=2(\text{a}+\text{b})(\text{b}+\text{c})(\text{c}+\text{a}).$

Solve the Linear Programming Problem graphically: Maximize $Z = 3x + 4y$ Subject to $\begin{array}{l}2 x+2 y \leq 80 \\ 2 x+4 y \leq 120\end{array}$