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Popular >

derivative of arctan(sin(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial y)(x^3y^4)

\frac{\partial}{\partial y} (x^{3} y^{4})

d/(dy)(cos(x^2)-y)

\frac{d}{d y} (cos (x^{2}) - y)

integral from-4 to 6 of 6

\int_{- 4}^{6} 6 d x

tangent of f(x)=-4x^2-4x+4,\at x=1 tangent of

f (x) = - 4 x^{2} - 4 x + 4, at x = 1

tangent of-(12)/((4x+1)^2)tangent of

- \frac{12}{( 4 x + 1 ) ^{2}}

Frequently Asked Questions (FAQ)

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