What is (\partial)/(\partial x)(5x^7cos(y^8)) ?

The answer to (\partial)/(\partial x)(5x^7cos(y^8)) is 35x^6cos(y^8)

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(\partial)/(\partial x)(5x^7cos(y^8))

\frac{\partial}{\partial x} (5 x^{7} cos (y^{8}))

35 x^{6} cos (y^{8})

Solution steps

\frac{\partial}{\partial x} (5 x^{7} cos (y^{8}))

Treat

y

as a constant

Take the constant out:

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

= 5 cos (y^{8}) \frac{\partial}{\partial x} (x^{7})

Apply the Power Rule:

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

= 5 cos (y^{8}) \cdot 7 x^{7 - 1}

Simplify

= 35 x^{6} cos (y^{8})

x \to 0 - lim (\frac{7}{x} - \frac{7}{∣ x ∣})

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

x^{4} - 17 x^{2} + 16

x \to 0 lim (x e^{- 2 x})

\int x^{13} d x

What is (\partial)/(\partial x)(5x^7cos(y^8)) ?
The answer to (\partial)/(\partial x)(5x^7cos(y^8)) is 35x^6cos(y^8)