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

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

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

\frac{\partial}{\partial x} (3 x^{2} \cdot 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)))

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

x \to 8 + lim (\frac{6 x}{x - 8})

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

\int x e^{7 x} d x

x^{2} + y^{2} = 25, y = 0

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