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Popular >

derivative of arctan(sin(4x))

Solution

derivative of

arctan (sin (4 x))

Solution

\frac{4 cos ( 4 x )}{sin ^{2} ( 4 x ) + 1}

Solution steps

\frac{d}{d x} (arctan (sin (4 x)))

Apply the chain rule:

\frac{1}{( sin ( 4 x ) ) ^{2} + 1} \frac{d}{d x} (sin (4 x))

= \frac{1}{( sin ( 4 x ) ) ^{2} + 1} \frac{d}{d x} (sin (4 x))

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

= \frac{1}{( sin ( 4 x ) ) ^{2} + 1} cos (4 x) \cdot 4

Simplify

\frac{1}{sin ^{2} ( 4 x ) + 1} cos (4 x) \cdot 4 : \frac{4 cos ( 4 x )}{sin ^{2} ( 4 x ) + 1}

= \frac{4 cos ( 4 x )}{sin ^{2} ( 4 x ) + 1}

Popular Examples

y^{''}+25y=-25sec^2(5x)

y^{^{''}} + 25 y = - 25 sec^{2} (5 x)

(\partial)/(\partial x)(2+xln(xy-7))

\frac{\partial}{\partial x} (2 + x ln (x y - 7))

derivative of x^2sqrt(x-1)

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

integral of (3x^2+8x-12)/(x^3+7x+12x)

\int \frac{3 x ^{2} + 8 x - 12}{x ^{3} + 7 x + 12 x} d x

integral of (3^{x+2})/(4^{x-1)}

\int \frac{3 ^{x + 2}}{4 ^{x - 1}} d x

Frequently Asked Questions (FAQ)

What is the derivative of arctan(sin(4x)) ?
The derivative of arctan(sin(4x)) is (4cos(4x))/(sin^2(4x)+1)
What is the first derivative of arctan(sin(4x)) ?
The first derivative of arctan(sin(4x)) is (4cos(4x))/(sin^2(4x)+1)