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Popular >

d/(dθ)(θcos(θ)sin(θ))

Solution

\frac{d}{d θ} (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

integral of (cos(θ))/(5+4cos(θ))

\int \frac{cos ( θ )}{5 + 4 cos ( θ )} d θ

d/(dy)(3x^2y+e^y)

\frac{d}{d y} (3 x^{2} y + e^{y})

derivative of (3x)/4 derivative of

\frac{3 x}{4}

(\partial)/(\partial x)((4x^4y^2+9)2)

\frac{\partial}{\partial x} ((4 x^{4} y^{2} + 9) 2)

integral of-4sin^2(x+2)

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

Frequently Asked Questions (FAQ)

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