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Popular >

derivative of sin(cos(sin(x)))

Solution

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

Solution

- cos (cos (sin (x))) sin (sin (x)) cos (x)

Solution steps

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

Apply the chain rule:

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

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

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

= cos (cos (sin (x))) (- sin (sin (x)) cos (x))

Simplify

= - cos (cos (sin (x))) sin (sin (x)) cos (x)

Popular Examples

(\partial)/(\partial x)(c/x)

\frac{\partial}{\partial x} (\frac{c}{x})

integral of 3x^2-cos(x)+C

\int 3 x^{2} - cos (x) + C d x

integral of x/(2021^x)

\int \frac{x}{202 1 ^{x}} d x

derivative of x^{11}h(x)

\frac{d}{d x} (x^{11} h (x))

expand-(2x)/((x^2+4)^2)expand

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

Frequently Asked Questions (FAQ)

What is the derivative of sin(cos(sin(x))) ?
The derivative of sin(cos(sin(x))) is -cos(cos(sin(x)))sin(sin(x))cos(x)
What is the first derivative of sin(cos(sin(x))) ?
The first derivative of sin(cos(sin(x))) is -cos(cos(sin(x)))sin(sin(x))cos(x)