What is (\partial)/(\partial x)(3x^2cos^2(x-y)) ?

The answer to (\partial)/(\partial x)(3x^2cos^2(x-y)) is 3(2xcos^2(x-y)-x^2sin(2(-y+x)))

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(\partial)/(\partial x)(3x^2cos^2(x-y))

\frac{\partial}{\partial x} (3 x^{2} cos^{2} (x - y))

3 (2 x cos^{2} (x - y) - x^{2} sin (2 (- y + x)))

Solution steps

\frac{\partial}{\partial x} (3 x^{2} cos^{2} (x - y))

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (x^{2} cos^{2} (x - y))

Apply the Product Rule:

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

f = x^{2}, g = cos^{2} (x - y)

= 3 (\frac{\partial}{\partial x} (x^{2}) cos^{2} (x - y) + \frac{\partial}{\partial x} (cos^{2} (x - y)) x^{2})

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

\frac{\partial}{\partial x} (cos^{2} (x - y)) = - sin (2 (- y + x))

= 3 (2 x cos^{2} (x - y) + (- sin (2 (- y + x))) x^{2})

Simplify

= 3 (2 x cos^{2} (x - y) - x^{2} sin (2 (- y + x)))

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

\frac{d}{d x} (\frac{3}{5 - x})

\frac{d}{d x} (cos (x) sec^{7} (x))

2 sin (x) + c e^{- x} cos (x)

\int 3 sin^{3} (x co) s^{2} x d x

What is (\partial)/(\partial x)(3x^2cos^2(x-y)) ?
The answer to (\partial)/(\partial x)(3x^2cos^2(x-y)) is 3(2xcos^2(x-y)-x^2sin(2(-y+x)))