Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

${:[h(x)=arcsin(4x)],[h^(')(x)=?]:} Choose 1 answer: (A) (1)/(sqrt(1-16x^(2))) (B) (4)/(sqrt(1-16x^(2))) (C) (1)/(sqrt(1+16x^(2))) (D) (4)/(sqrt(1+16x^(2)))$

$\begin{array}{l} h(x)=\arcsin (4 x) \\ h^{\prime}(x)=? \end{array}$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{\sqrt{1-16 x^{2}}}$ $\newline$ (B) $\frac{4}{\sqrt{1-16 x^{2}}}$ $\newline$ (C) $\frac{1}{\sqrt{1+16 x^{2}}}$ $\newline$ (D) $\frac{4}{\sqrt{1+16 x^{2}}}$

View step-by-step help

View step-by-step help

Find derivatives of inverse trigonometric functions

Full solution

Q.

\begin{array}{l} h(x)=\arcsin (4 x) \\ h^{\prime}(x)=? \end{array}

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{\sqrt{1-16 x^{2}}}

\newline

(B)

\frac{4}{\sqrt{1-16 x^{2}}}

\newline

(C)

\frac{1}{\sqrt{1+16 x^{2}}}

\newline

(D)

\frac{4}{\sqrt{1+16 x^{2}}}

Apply Chain Rule: To find the derivative of $h(x) = \arcsin(4x)$ , we use the chain rule.
Derivative of arcsin(u): The derivative of $\arcsin(u)$ with respect to $u$ is $\frac{1}{\sqrt{1-u^2}}$ . Here, $u = 4x$ .
Calculate $\frac{du}{dx}$ : Using the chain rule, $h'(x) = \frac{d}{dx}(\arcsin(4x)) = \frac{d}{dx}(\arcsin(u)) \cdot \frac{du}{dx}$ .
Plug in Derivatives: We calculate $\frac{du}{dx}$ where $u = 4x$ . So, $\frac{du}{dx} = 4$ .
Simplify Expression: Now, plug in the derivative of $u$ and the derivative of $\arcsin(u)$ into the chain rule formula. $\newline$ $h'(x) = \frac{1}{\sqrt{1-(4x)^2}} \times 4$ .
Simplify Expression: Now, plug in the derivative of $u$ and the derivative of $\arcsin(u)$ into the chain rule formula. $\newline$ $h'(x) = \frac{1}{\sqrt{1-(4x)^2}} \times 4$ . Simplify the expression to get the final derivative. $\newline$ $h'(x) = \frac{4}{\sqrt{1-16x^2}}$ .

More problems from Find derivatives of inverse trigonometric functions

Question

\lim_{\theta \rightarrow \frac{\pi}{2}} \tan ^{2}(\theta)[1-\sin (\theta)]

\newline

1

\newline

0

\newline

\frac{1}{2}

\newline

-2

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{\sin ^{2}(2 \theta)}{1-\sin ^{2}(\theta)}

\newline

1

\newline

1

\newline

2

\newline

4

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{x \rightarrow 3} \frac{x-3}{\sqrt{4 x+4}-4}

\newline

1

\newline

-4

\newline

1

\newline

2

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{x \rightarrow-4} \frac{7 x+28}{x^{2}+x-12}

\newline

1

\newline

1

\newline

7

\newline

-1

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{x \rightarrow-3} \frac{x+3}{4-\sqrt{2 x+22}}

\newline

1

\newline

-3

\newline

-4

\newline

-\frac{3}{4}

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{x \rightarrow 1} \frac{\sqrt{5 x+4}-3}{x-1}

\newline

1

\newline

\frac{3}{5}

\newline

\frac{5}{6}

\newline

1

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{x \rightarrow-2} \frac{x^{3}+3 x^{2}+2 x}{x+2}

\newline

1

\newline

6

\newline

0

\newline

2

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot ^{2}(x)}{1-\sin (x)}

\newline

1

\newline

-1

\newline

-\frac{\pi}{2}

\newline

2

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin (2 x)}{\cos (x)}

\newline

1

\newline

\frac{1}{2}

\newline

1

\newline

2

\newline

(D) The limit doesn't exist

Posted 9 months ago

Question

\lim _{\theta \rightarrow \frac{\pi}{4}} \frac{\cos (2 \theta)}{\sqrt{2} \cos (\theta)-1}

\newline

1

\newline

2

\newline

\frac{1}{2}

\newline

\sqrt{2}

\newline

(D) The limit doesn't exist

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant