What is (\partial)/(\partial x)(10r^2sin(2x)) ?

The answer to (\partial)/(\partial x)(10r^2sin(2x)) is 20r^2cos(2x)

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(\partial)/(\partial x)(10r^2sin(2x))

\frac{\partial}{\partial x} (10 r^{2} sin (2 x))

20 r^{2} cos (2 x)

Solution steps

\frac{\partial}{\partial x} (10 r^{2} sin (2 x))

Treat

r

as a constant

Take the constant out:

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

= 10 r^{2} \frac{\partial}{\partial x} (sin (2 x))

Apply the chain rule:

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

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

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

= 10 r^{2} cos (2 x) \cdot 2

Simplify

= 20 r^{2} cos (2 x)

\int (2 x^{2} - 6 x) e^{2 x} d x

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

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

\int (4 - 3 x)^{7} d x

cos (2 (t - \frac{π}{2}))

What is (\partial)/(\partial x)(10r^2sin(2x)) ?
The answer to (\partial)/(\partial x)(10r^2sin(2x)) is 20r^2cos(2x)