Differentiate the following functions with respect to x: 3^ x^2+2… - Vidyadip

Question

Differentiate the following functions with respect to x:
$3^{\text{x}^2+2\text{x}}$

✓

Answer

Consider $\text{y}=3^{\text{x}^2+2\text{x}}$
Differentiate it with respect to x,
$\frac{\text{d}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(3^{\text{x}^2+2\text{x}}\Big)$
$=3^{\text{x}^2+2\text{x}}\times\log3\frac{\text{d}}{\text{dx}}(\text{x}^2+2\text{x})$
[Using chain rule]
$=(2\text{x}+2)\log3\times3^{\text{x}^2+2\text{x}}$
Hence, the solution is, $\frac{\text{d}}{\text{dx}}\big(3\text{x}^2+2\text{x}\big)=(2\text{x}+2)\log3\times3^{\text{x}^2+2\text{x}}$

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" 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

Find the vector and cartesian equations of a plane passing through the point (1, -1, 1) and normal to the line joining the points (1, 2, 5) and (-1, 3, 1)

Find the magnitude of $\vec{\text{a}}=\big(3\hat{\text{k}}+4\hat{\text{j}}\big)\times(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}).$

Differentiate w.r.t. x the function in Exercise:
$(5\text{x})^{3\cos2\text{x}}$

Find the matrix A such that
$\text{A}=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}=\begin{bmatrix}-7&-8&-9\\2&4&6\\11&10&9\end{bmatrix}$

Solve the following differential equations:

$\text{ye}^{\frac{\text{x}}{\text{y}}}\text{dx}=(\text{xe}^{\frac{\text{x}}{\text{y}}}+\text{y}^2)\text{dy, y}\neq0$

Let f be a function from R to R, such that f(x) = cos(x + 2). Is f invertible? Justify your answer.

A vector $\vec{\text{r}}$ is inclined to x-axis at 45º and y-axis at 60º. If $|\vec{\text{r}}|=8$ units, find $\vec{\text{r}}$.

show that $\text{f}\text{(x)}=\begin{cases}\frac{\text{x}-|\text{x}|}{2}, & \text{when} \text{ x}\neq 0\\2, & \text{when}\text{ x} = 0\end{cases}$ is discontinuous at x = 0.

Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\text{x}^{\frac{2}{3}}\text{ on }[-1,1]$

Write the difference between maximum and minimum values of $\sin^{-1}\text{x}$ for $\text{x}\in[-1,1].$