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Popular >

derivative of (sin(x+cos(x))^3)

Solution

\frac{d}{d x} ((sin (x) + cos (x))^{3})

Solution

3 (1 + sin (2 x)) (cos (x) - sin (x))

Solution steps

\frac{d}{d x} ((sin (x) + cos (x))^{3})

Apply the chain rule:

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

= 3 (sin (x) + cos (x))^{2} \frac{d}{d x} (sin (x) + cos (x))

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

= 3 (sin (x) + cos (x))^{2} (cos (x) - sin (x))

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

= 3 (1 + sin (2 x)) (cos (x) - sin (x))

Popular Examples

derivative of (1/2 x)^3 derivative of

(\frac{1}{2} x)^{3}

derivative of (3x^2+4x+1^{10})

\frac{d}{d x} ((3 x^{2} + 4 x + 1)^{10})

integral from 4 to 8 of x/(x^2+6x+13)

\int_{4}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

derivative of 1/a sin(b+ax)

\frac{d}{d x} (\frac{1}{a} sin (b + a x))

integral of e^{5x}cos(x)

\int e^{5 x} cos (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (sin(x+cos(x))^3) ?
The derivative of (sin(x+cos(x))^3) is 3(1+sin(2x))(cos(x)-sin(x))
What is the first derivative of (sin(x+cos(x))^3) ?
The first derivative of (sin(x+cos(x))^3) is 3(1+sin(2x))(cos(x)-sin(x))