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Popular >

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

Solution

derivative of

(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))

Graph

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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))