Differentiate the following functions with respect to x: 3^ e^ x - Vidyadip

Question

Differentiate the following functions with respect to x:
$3^{\text{e}^{\text{x}}}$

✓

Answer

Let, $\text{y}=3^{\text{e}^{\text{x}}}$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(3^{\text{e}^\text{x}}\Big)$
$=3^{\text{e}^\text{x}}\log3\frac{\text{d}}{\text{dx}}\big(\text{e}^\text{x}\big)$
[Using chain rule]
$=\text{e}^\text{x}\times3^{\text{e}^\text{x}}\log3 $
So,
$\frac{\text{d}}{\text{dx}}\Big(3^{\text{e}^\text{x}}\Big)=\text{e}^\text{x}\times3^{\text{e}^\text{x}}\log3$

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

Let * be a binary operation on $Q_0$ (set of non-zero rational numbers) defined by $\text{a}\ ^* \ \text{b}=\frac{\text{ab}}{5}$ for all $\text{a, b}\in\text{Q}_0.$ Show that * is commutative as well as associative. Also, find its identity element if it exists.

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases:
$\tan^{-1}\big(\text{x}^2+\text{y}^2\big)=\text{a}$

The p.d.f. of a continuous r.v. $X$ is given by $f ( x )=\frac{1}{2 a}$, for $0< x <2 a$ and $=0$, otherwise. Show that $P \left( X <\frac{a}{2}\right)= P \left( X >\frac{3 a}{2}\right)$

Find the area of the ellipse $\frac{x^2}{36}+\frac{y^2}{64}=1$, using integration

If $2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$, then find the value of $x$.

Diffrentiate the following w. r. t. x.

$\cos ^{-1}\left(\frac{3 \cos \left(e^x\right)+2 \sin \left(e^x\right)}{\sqrt{13}}\right)$

If a, b, c are non-zero real numbers and if the system of equations

(a - 1)x = y + z

(b - 1)y = z + x

(c - 1)z = x + y

has a non-trivial solution, then prove that ab + bc + ca = abc.

If $\text{A}=\begin{bmatrix}1&2\\0&3 \end{bmatrix}$ is written as B + C, where B is a symmetric matrix and C is a skew- symmetric matrix, then B is equal to.

$\int_{-\pi / 4}^{\pi / 4} \frac{1}{1-\sin x} \cdot d x$

In $\triangle ABC$, prove that $\frac{\cos 2 A }{ a ^2}-\frac{\cos 2 c }{ c ^2}=\frac{1}{ a ^2}-\frac{1}{ c ^2}$