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

The answer to (\partial)/(\partial x)(cos^2(x)y) is -ysin(2x)

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

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

- y sin (2 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y \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)

= y \cdot 2 cos (x) (- sin (x))

Simplify

y \cdot 2 cos (x) (- sin (x)) : - y sin (2 x)

= - y sin (2 x)

\frac{d}{d a} (sec (a) \cdot tan (a) \cdot cos (a) \cdot csc (a))

\frac{1}{( x - 2 ) ( x + 1 )}

\int \frac{e ^{9 x}}{e ^{9 x} + 1} d x

f (x) = sin (x + 1)

\int 3 y^{2} \frac{1}{2 y} tan (2 y x) d x

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