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

The answer to (\partial)/(\partial x)(2x^3cos(xy)) is 2(3x^2cos(xy)-x^3ysin(xy))

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(\partial)/(\partial x)(2x^3cos(xy))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3}, g = cos (x y)

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

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

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

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

Simplify

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

x \to 0 lim (\frac{1}{3 ^{x}})

f (x) = x^{3} + 5 x + 7

\frac{4}{s ^{2} + 2 s + 4}

\frac{d}{d x} (\frac{1}{ln ( x + 1 + x ^{2} )})

\frac{\partial}{\partial s} (- (s^{2} + t^{2}))

What is (\partial)/(\partial x)(2x^3cos(xy)) ?
The answer to (\partial)/(\partial x)(2x^3cos(xy)) is 2(3x^2cos(xy)-x^3ysin(xy))