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Popular >

d/(dθ)(sin(θ)cos(θ))

Solution

\frac{d}{d θ} (sin (θ) cos (θ))

Solution

cos (2 θ)

Solution steps

\frac{d}{d θ} (sin (θ) cos (θ))

Apply the Product Rule:

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

f = sin (θ), g = cos (θ)

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

\frac{d}{d θ} (sin (θ)) = cos (θ)

\frac{d}{d θ} (cos (θ)) = - sin (θ)

= cos (θ) cos (θ) + (- sin (θ)) sin (θ)

Simplify

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

= cos (2 θ)

Graph

Popular Examples

integral of e^{sin(pi)x}cos(pi)x

\int e^{s i n (π) x} cos (π) x d x

limit as x approaches 1 of x^2-2x-1

x \to 1 lim (x^{2} - 2 x - 1)

integral of (cos(x))/(4+sin^2(x))

\int \frac{cos ( x )}{4 + sin ^{2} ( x )} d x

integral of (432)/(w^2sqrt(144-w^2))

\int \frac{432}{w ^{2} 144 - w ^{2}} d w

f (x) = e^{3 x^{2}}

Frequently Asked Questions (FAQ)

What is the d/(dθ)(sin(θ)cos(θ)) ?
The d/(dθ)(sin(θ)cos(θ)) is cos(2θ)
What is the first d/(dθ)(sin(θ)cos(θ)) ?
The first d/(dθ)(sin(θ)cos(θ)) is cos(2θ)