What is (\partial)/(\partial x)(r^2cos^2(x)) ?

The answer to (\partial)/(\partial x)(r^2cos^2(x)) is -r^2sin(2x)

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(\partial)/(\partial x)(r^2cos^2(x))

\frac{\partial}{\partial x} (r^{2} cos^{2} (x))

- r^{2} sin (2 x)

Solution steps

\frac{\partial}{\partial x} (r^{2} cos^{2} (x))

Treat

r

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= r^{2} \frac{\partial}{\partial x} (cos^{2} (x))

Apply the chain rule:

2 cos (x) \frac{\partial}{\partial x} (cos (x))

= 2 cos (x) \frac{\partial}{\partial x} (cos (x))

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

= r^{2} \cdot 2 cos (x) (- sin (x))

Simplify

r^{2} \cdot 2 cos (x) (- sin (x)) : - r^{2} sin (2 x)

= - r^{2} sin (2 x)

\int_{- 6}^{6} (6 - ∣ x ∣) d x

f (x) = tan (x^{2})

\frac{d}{d x} ((2 x - 1)^{2} ln (3 x + 4))

\int 20 e^{5 x} d x

\int n x d x

What is (\partial)/(\partial x)(r^2cos^2(x)) ?
The answer to (\partial)/(\partial x)(r^2cos^2(x)) is -r^2sin(2x)