What is (\partial)/(\partial x)(x^4cos(xy)) ?

The answer to (\partial)/(\partial x)(x^4cos(xy)) is 4x^3cos(xy)-x^4ysin(xy)

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(\partial)/(\partial x)(x^4cos(xy))

\frac{\partial}{\partial x} (x^{4} cos (x y))

4 x^{3} cos (x y) - x^{4} y sin (x y)

Solution steps

\frac{\partial}{\partial x} (x^{4} cos (x y))

Treat

y

as a constant

Apply the Product Rule:

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

f = x^{4}, g = cos (x y)

= \frac{\partial}{\partial x} (x^{4}) cos (x y) + \frac{\partial}{\partial x} (cos (x y)) x^{4}

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} cos (x y) + (- sin (x y) y) x^{4}

Simplify

= 4 x^{3} cos (x y) - x^{4} y sin (x y)

x \to \infty lim (7)

\frac{d}{d x} ((e^{x})^{- 1})

\frac{( 3 x + 5 )}{1 + x}

ln (1 + 2 x)

\int ln^{3} (2 x) d x

What is (\partial)/(\partial x)(x^4cos(xy)) ?
The answer to (\partial)/(\partial x)(x^4cos(xy)) is 4x^3cos(xy)-x^4ysin(xy)