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 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

Let $A = \{-1, 0, 1, 2\}, B = \{-4, -2, 0, 2\}$ and $f, g : A \rightarrow B$ be the functions defined by $f(x) = x^2 - x, x \in A$ and $g(x) = 2\left| {x - \frac{1}{2}} \right| - 1,x \in A.$ Are $f$ and $g$ equal? Justify your answer. $($Hint: One may note that two functions $f : A \rightarrow B$ and $g : A \rightarrow B$ such that$ f(a) = g(a) \forall$ a $\in A,$ are called equal functions$).$

Differentiate the following functions with respect to x:
$\sin^2(2\text{x}+1)$

A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?

Assume that the chances of a patient having a heart attack is $40\%. $ It is also assumed that a meditation and yoga course reduce the risk of heart attack by $30\%$ and prescription of certain drug reduces its chances by $25\%$. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

Find the vector equation of the plane with intercepts 3, -4 and 2 on x, y and z-axis respectively.

Find gof and fog when $f : R \rightarrow R$ and $g : R \rightarrow R$ are defined by:
$f(x) = x^2 + 2x - 3$ and $g(x) = 3x - 4$

Find the second order derivatives of the following functions:$\sin(\log\text{x})$

Evaluate the following integrals:
$\int_{1}^\limits{2}\frac{3\text{x}}{9\text{x}^2-1}\text{ dx}$

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases: $xy = c^2$

Find the length of the perpendicular drow from the point (5, 4, -1) to the line $\vec{\text{r}}=\hat{\text{i}}+\lambda\big(2\hat{\text{i}}+9\hat{\text{j}}+5\hat{\text{k}}\big).$