What is (\partial)/(\partial x)(8x^2cos(5)x^3) ?

The answer to (\partial)/(\partial x)(8x^2cos(5)x^3) is 40cos(5)x^4

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(\partial)/(\partial x)(8x^2cos(5)x^3)

\frac{\partial}{\partial x} (8 x^{2} cos (5) x^{3})

40 cos (5) x^{4}

Solution steps

\frac{\partial}{\partial x} (8 x^{2} cos (5) x^{3})

Simplify

8 x^{2} cos (5) x^{3} : 8 cos (5) x^{5}

= \frac{\partial}{\partial x} (8 cos (5) x^{5})

Take the constant out:

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

= 8 cos (5) \frac{\partial}{\partial x} (x^{5})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 8 cos (5) \cdot 5 x^{5 - 1}

Simplify

= 40 cos (5) x^{4}

\frac{d}{d x} (\frac{ln ( x )}{e ^{x}})

\int_{0}^{2} \frac{1}{9 - x ^{2}} d x

f (x) = 3 x^{4}

x \to 7 lim (\frac{x ^{2} - 4}{7 - x})

\int arctan (5 t) d t

What is (\partial)/(\partial x)(8x^2cos(5)x^3) ?
The answer to (\partial)/(\partial x)(8x^2cos(5)x^3) is 40cos(5)x^4