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Popular >

derivative of cos(arcsin(4x))

Solution

\frac{d}{d x} (cos (arcsin (4 x)))

Solution

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

Solution steps

\frac{d}{d x} (cos (arcsin (4 x)))

Simplify

cos (arcsin (4 x)) : 1 - 16 x^{2}

= \frac{d}{d x} (1 - 16 x^{2})

Apply the chain rule:

\frac{1}{2 1 - 16 x ^{2}} \frac{d}{d x} (1 - 16 x^{2})

= \frac{1}{2 1 - 16 x ^{2}} \frac{d}{d x} (1 - 16 x^{2})

\frac{d}{d x} (1 - 16 x^{2}) = - 32 x

= \frac{1}{2 1 - 16 x ^{2}} (- 32 x)

Simplify

\frac{1}{2 1 - 16 x ^{2}} (- 32 x) : - \frac{16 x}{1 - 16 x ^{2}}

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

Popular Examples

derivative of 14x^6-5x^4+15x^2-8

\frac{d}{d x} (14 x^{6} - 5 x^{4} + 15 x^{2} - 8)

derivative of f(x)=xe^{3x^2}+1 derivative of

f (x) = x e^{3 x^{2}} + 1

tangent of 4/(x^5)-1/(x^2)tangent of

\frac{4}{x ^{5}} - \frac{1}{x ^{2}}

integral of (cos(x))/(1+8sin(x))

\int \frac{cos ( x )}{1 + 8 sin ( x )} d x

(dy)/(dx)=(x/y)

\frac{d y}{d x} = (\frac{x}{y})

Frequently Asked Questions (FAQ)

What is the derivative of cos(arcsin(4x)) ?
The derivative of cos(arcsin(4x)) is -(16x)/(sqrt(1-16x^2))
What is the first derivative of cos(arcsin(4x)) ?
The first derivative of cos(arcsin(4x)) is -(16x)/(sqrt(1-16x^2))