What is the derivative of {r}(x*cos(x)) ?

The derivative of {r}(x*cos(x)) is cos(x) derivative of {r}(x)-sin(x){r}(x)

What is the first derivative of {r}(x*cos(x)) ?

The first derivative of {r}(x*cos(x)) is cos(x) derivative of {r}(x)-sin(x){r}(x)

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Popular >

\frac{d}{d x} (r (x) \cdot cos (x))

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

Solution steps

\frac{d}{d x} (r (x) cos (x))

Apply the Product Rule:

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

f = r (x), g = cos (x)

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

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

n = 0 \sum \infty (- \frac{1}{2})^{n - 1}

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

f (t) = \frac{t}{2}

\frac{d}{d x} (x^{0.25})

\frac{d}{d x} (4 x - 2)

What is the derivative of {r}(x*cos(x)) ?
The derivative of {r}(x*cos(x)) is cos(x) derivative of {r}(x)-sin(x){r}(x)
What is the first derivative of {r}(x*cos(x)) ?
The first derivative of {r}(x*cos(x)) is cos(x) derivative of {r}(x)-sin(x){r}(x)