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

Question

Differentiate the following functions with respect to x:
$3\text{e}^{-3\text{x}}\log(1+\text{x})$

✓

Answer

Consider $\text{y}=3\text{e}^{-3\text{x}}\log(1+\text{x})$
Differentiating it with respect to x and applying the chain and product rule, we get
$\frac{\text{dy}}{\text{dx}}=3\frac{\text{d}}{\text{dx}}\big[3\text{e}^{-3\text{x}}\log(1+\text{x})\big]$
$\frac{\text{dy}}{\text{dt}}=3\Big(\text{e}^{-3\text{x}}\frac{1}{1+\text{x}}+\log(1+\text{x})\big(-3\text{e}^{-3\text{x}}\big)\Big)$
$=3\Big(\frac{\text{e}^{-3\text{x}}}{1+\text{x}}-3\log(1+\text{x})\Big)$
The solution is,
$=3\text{e}^{-3\text{e}}\Big(\frac{1}{1+\text{x}}-3\log(1-\text{x})\Big)$

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 "5 Marks Questions" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{x}=\text{a}\sin\text{t}-\text{b}\cos\text{t},\text{y}=\text{a}\cos\text{t}+\text{b}\sin\text{t},$ Prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\frac{\text{x}^2+\text{y}^2}{\text{y}^2}$

Find the area of the region bounded by the ellipse $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} = 1$.

Evaluate the following integrals:$\int\frac{\text{x}^2+1}{\text{x}^2-5\text{x}+6}\text{ dx}$

$\int\frac{3\text{x}+5}{\sqrt{7\text{x}+9}}\text{dx}$

A box manufacturer makes large and small boxes from a large piece of cardboard. The large boxes require $4$ sq. metre per box while the small boxes require $3$ sq. metre per box. The manufacturer is required to make at least three large boxes and at least twice as many small boxes as large boxes. If $60$ sq. metre of cardboard is in stock, and if the profits on the large and small boxes are Rs. $3$ and Rs. $2$ per box, how many of each should be made in order to maximize the total profit?

Find $\frac{\text{dy}}{\text{dx}} \text{if y = }\sin^{-1}\bigg[\frac{6x - 4\sqrt{1 - 4x}^{2}}{5}\bigg]$

$\text{if} \overrightarrow{\text{r}} = x\hat{\text{i}} + y\hat{\text{j}} + z\hat{\text{k}}, \text{find} \overrightarrow(\text{r} \times \hat{\text{i}}). (\overrightarrow{\text{r}} \times \text{j}) + xy$

Evaluate the following integrals:
$\int\limits^{\pi}_0\frac{\text{x}\sin\text{x}}{1+\sin\text{x}}\text{ dx}$

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}+\frac{1+\text{y}^2}{\text{y}}=0$

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of A and ₹ 80 on each piece of type ₹ 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?