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Popular Calculus >

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

Solution

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

Solution

cos (2 x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = cos (x)

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

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

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

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

Simplify

cos (x) cos (x) + (- sin (x)) sin (x) : cos (2 x)

= cos (2 x)

Graph

Popular Examples

implicit (dy)/(dx),xy=15

im pl i c i t \frac{d y}{d x}, x y = 15

(\partial)/(\partial x)(2sin(x^2+y^2))

\frac{\partial}{\partial x} (2 sin (x^{2} + y^{2}))

d/(dθ)(8sin(θ))

\frac{d}{d θ} (8 sin (θ))

integral of 17x^3e^x

\int 17 x^{3} e^{x} d x

derivative of sqrt(-5+9x)

d er i v a t i v e - 5 + 9 x

Frequently Asked Questions (FAQ)

What is the derivative of (sin(x)(cos(x))) ?
The derivative of (sin(x)(cos(x))) is cos(2x)
What is the first derivative of (sin(x)(cos(x))) ?
The first derivative of (sin(x)(cos(x))) is cos(2x)