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Popular Calculus >

d/(dθ)({r}(θ)(1-cos(θ)))

Solution

\frac{d}{d θ} (r (θ) (1 - cos (θ)))

Solution

\frac{d}{d θ} (r (θ)) (1 - cos (θ)) + sin (θ) r (θ)

Solution steps

\frac{d}{d θ} (r (θ) (1 - cos (θ)))

Apply the Product Rule:

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

f = r (θ), g = 1 - cos (θ)

= \frac{d}{d θ} (r (θ)) (1 - cos (θ)) + \frac{d}{d θ} (1 - cos (θ)) r (θ)

\frac{d}{d θ} (1 - cos (θ)) = sin (θ)

= \frac{d}{d θ} (r (θ)) (1 - cos (θ)) + sin (θ) r (θ)

Popular Examples

derivative of ln((3x+1(x+2)^2))

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

derivative of e^{-2x}cos(x)

\frac{d}{d x} (e^{- 2 x} cos (x))

tangent of y=3+4x+7xe^x

t an g e n t y = 3 + 4 x + 7 x e^{x}

integral of tan(x)(4cos(x)+8sec(x))

\int tan (x) (4 cos (x) + 8 sec (x)) d x

(dy)/(dx)+y^5x+6y=0

\frac{d y}{d x} + y^{5} x + 6 y = 0

Frequently Asked Questions (FAQ)

What is the d/(dθ)({r}(θ)(1-cos(θ))) ?
The d/(dθ)({r}(θ)(1-cos(θ))) is d/(dθ)({r}(θ))(1-cos(θ))+sin(θ){r}(θ)
What is the first d/(dθ)({r}(θ)(1-cos(θ))) ?
The first d/(dθ)({r}(θ)(1-cos(θ))) is d/(dθ)({r}(θ))(1-cos(θ))+sin(θ){r}(θ)