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Popular >

derivative of sin(θ)cos(θ)

Solution

derivative of

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)

Popular Examples

integral of-sec(x)

\int - sec (x) d x

limit as x approaches-27 of 6/(x+27)

x \to - 27 lim (\frac{6}{x + 27})

integral from 0 to-0.4 of 400x

\int_{0}^{- 0.4} 400 x d x

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

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

integral of y^6

\int y^{6} d y

Frequently Asked Questions (FAQ)

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