Differentiate the following w.r.t.x: ( +e^ x ),x>0 - Vidyadip

Question

Differentiate the following w.r.t.x: $\cos({\log\text{x}}+\text{e}^{\text{x}}),\text{x}>0$

✓

Answer

$\text{Let y}=\cos({\log\text{x}}+\text{e}^{\text{x}})$
$\therefore\ \frac{\text{dy}}{\text{dx}} =-\sin(\log\text{x}+\text{e}^\text{x})\frac{\text{d}}{\text{dx}}(\log\text{x}+\text{e}^\text{x})$
$ =-\sin(\log\text{x}+\text{e}^\text{x}).\Big(\frac{1}{\text{x}}+\text{e}^\text{x}\Big)$
$ =-\Big(\frac{1}{\text{x}}+\text{e}^\text{x}\Big)\sin(\log\text{x}+\text{e}^\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 "2 Marks Questions" 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

If $A$ is a square matrix such that $|A| = 2$, write the value of $\big|\text{A}\text{A}^{\text{T}}\big|.$

Let A = {1, 2, 3, 4} and B = {a, b} be two sets. Write the total number of onto functions from A to B.

Write the position vector of a point dividing the line segment joining points A and B with position vectors $\vec{\text{a}}\text{ and }\vec{\text{b}}$ externally in the ratio 1 : 4, where $\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=-\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$.

Give example of matrices:
A and B such that AB = 0 but BA ≠ 0

The total revenue received from the sale of x units of a product is given by $R(x) = 13x^2 + 26x + 15$. Find the marginal revenue when $x = 7$.

Find the integral: $\int \frac{2-3 \sin x}{\cos ^{2} x} d x$

Find the position vector of the mid-point of the vector joining the points P(2, 3, 4) and Q(4, 1, -2).

Integrate the function: $\frac{{\sin x}}{{1 + \cos x}}$

If x and y are connected parametrically by the equation x = a ($\theta$ – sin $\theta$), y = a (1 + cos $\theta$) without eliminating the parameter. Find $\frac{d y}{d x}$.

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=\sqrt{3}$ and $\vec{\text{a}}.\vec{\text{b}}=1,$ find the angle between.