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Popular >

derivative of θcos(θ)sin(θ)

Solution

derivative of

θ cos (θ) sin (θ)

Solution

cos (θ) sin (θ) + θ cos (2 θ)

Solution steps

\frac{d}{d θ} (θ cos (θ) sin (θ))

Apply the Product Rule:

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

f = θ, g = cos (θ) sin (θ)

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

\frac{d}{d θ} (θ) = 1

\frac{d}{d θ} (cos (θ) sin (θ)) = cos (2 θ)

= 1 \cdot cos (θ) sin (θ) + cos (2 θ) θ

Simplify

= cos (θ) sin (θ) + θ cos (2 θ)

Popular Examples

x^2(dy)/(dx)-y^3=xy

x^{2} \frac{d y}{d x} - y^{3} = x y

derivative of x/(1-x^2)

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

integral of (x^2)/(x^3-3)

\int \frac{x ^{2}}{x ^{3} - 3} d x

integral from 0 to 5 of 0.2x

\int_{0}^{5} 0.2 x d x

sum from n=1 to infinity of n(n+1)

n = 1 \sum \infty n (n + 1)

Frequently Asked Questions (FAQ)

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