What is (\partial)/(\partial x)(2x^4y+sin(x^4)) ?

The answer to (\partial)/(\partial x)(2x^4y+sin(x^4)) is 8yx^3+cos(x^4)*4x^3

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(\partial)/(\partial x)(2x^4y+sin(x^4))

\frac{\partial}{\partial x} (2 x^{4} y + sin (x^{4}))

8 y x^{3} + cos (x^{4}) \cdot 4 x^{3}

Solution steps

\frac{\partial}{\partial x} (2 x^{4} y + sin (x^{4}))

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x^{4} y) + \frac{\partial}{\partial x} (sin (x^{4}))

\frac{\partial}{\partial x} (2 x^{4} y) = 8 y x^{3}

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

= 8 y x^{3} + cos (x^{4}) \cdot 4 x^{3}

\int \frac{arcsin ( ln ( x ) )}{x} d x

\frac{1}{cos ( \frac{x}{2} )}

\frac{d}{d x} (- \frac{2 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}})

(x - 5) (x + 4) (x + 6)

\frac{d}{d x} (\frac{( x + 2 ) ( x + 1 )}{2 x - 1})

What is (\partial)/(\partial x)(2x^4y+sin(x^4)) ?
The answer to (\partial)/(\partial x)(2x^4y+sin(x^4)) is 8yx^3+cos(x^4)*4x^3