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Popular >

d/(dθ)(r(θ)cos(θ))

Solution

\frac{d}{d θ} (r (θ) cos (θ))

Solution

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

Solution steps

\frac{d}{d θ} (r (θ) cos (θ))

Apply the Product Rule:

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

f = r (θ), g = cos (θ)

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

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

Simplify

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

Popular Examples

3x+y-2+y^'(x-1)=0

3 x + y - 2 + y^{^{'}} (x - 1) = 0

integral from 1 to 2 of pi(2-1/2 x)^2

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

tangent of x=fxx^3-4x,(-2,0)tangent of

x = f x x^{3} - 4 x, (- 2, 0)

limit as x approaches 10-of 9/(x-10)

x \to 10 - lim (\frac{9}{x - 10})

derivative of sqrt((7-x^2))

\frac{d}{d x} ((7 - x^{2}))

Frequently Asked Questions (FAQ)

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