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

Question

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

✓

Answer

Let $\text{y}=\text{e}^{\tan \text{x}}$
Differentiate it with respect to x we get,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(\text{e}^{\tan\text{x}}\Big)$
$=\text{e}^{\tan\text{x}}\frac{\text{d}}{\text{dx}}(\tan\text{x})$
[Using chain rule]
$=\text{e}^{\tan\text{x}}\times\sec^2\text{x} $
So, $\frac{\text{d}}{\text{dx}}\big(\text{e}^{\tan\text{x}}\big)=\sec^2\text{xe}^{\tan\text{x}}$

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 Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If f : A → B and g : B → C are onto functions, show that gof is a onto function.

Solve: $\cos\big(\sin^{-1}\text{x}\big)=\frac{1}{6}$

Using Rolle's theorem, find points on the curve $\text{y}=16-\text{x}^2,\text{x}\in[-1,1],$ where tagent is parallel to x-axis.

Evaluate the following definite integrals:$\int_{0}^\limits{\frac{\pi}{2}}\text{x}^2\cos2\text{x}\text{ dx}$

Find the inverse of each of the following matrices $($if they exist$)$ : $\left[\begin{array}{lll}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$

Solve:
$\tan^{-1}\text{x}+2\cot^{-1}\text{x}=\frac{2\pi}{3}$

Find $\frac{d y}{d x}$ if

$x^3+x^2 y+x y^2+y^3=81$

Classify the following functions as injection, surjection or bijection:
f : Z → Z, defined by f(x) = x - 5

A bag contains 4 red and 6 black balls. Three balls are drawn at random. Find the probability distribution of the number of red balls.

Prove that: $\int_0^{ a } f (x) d x=\int_0^{ a } f ( a -x) d x$. Hence find $\int_0^{\frac{\pi}{2}} \sin ^2 x d x$