Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
Question
Differentiate cos–1(ex) w.r.t. x.
✓

Answer

Let $y = cos^{–1} (e^x)$.
Using the chain rule, we have
$\frac{d y}{d x}=\frac{-1}{\sqrt{1-\left(e^{x}\right)^{2}}} \cdot \frac{d}{d x}\left(e^{x}\right)=\frac{-e^{x}}{\sqrt{1-e^{2 x}}}$

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 "1 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 integral: $\int \frac{d x}{x^{2}-6 x+13}$
→
If $\vec{\text{a}}, \text{ }\vec{\text{b}},\text{ } \vec{\text{c}}$ are unit vectors such that $\vec{\text{a}}, \text{ }\vec{\text{b}}, \text{ }\vec{\text{c}}\text{ }=\vec{0},$ then write the value of $\vec{\text{a}} \text{ . }\vec{\text{b}} + \vec{\text{b}} \text{ . } \text{ }\vec{\text{c}} +\vec{\text{c}} . \vec{\text{a}}\text{ }.$
→
The total cost C(x) in rupees associated with the production of x units of an item given by c(x) = 0.007x3 - 0.003x2 + 15x + 4000. Find the marginal cost when 17 units are produced.
→
For each of the differential equations given below, indicate its order and degree (if defined).
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^2-6\text{y}=\log\text{x}$
→
Determine order and degree (if defined) of differential equations given in Exercise.
y' + 5y = 0
→
Evaluate $\int_{2}^{3} x^{2} d x$
→
Find the integral: $\int \frac{1-\sin x}{\cos ^{2} x} d x$
→
Construct a 4 × 3 matrix whose element are:
aij = i
→
Find $\int \frac{x^{2}+1}{x^{2}-5 x+6} d x$
→
Write the degree of the differrntial equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{\frac{1}{4}}+\text{x}^{\frac{1}{5}}=0.$ 
→