What is (\partial)/(\partial x)(x^4-4x^5y) ?

The answer to (\partial)/(\partial x)(x^4-4x^5y) is 4x^3-20yx^4

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(\partial)/(\partial x)(x^4-4x^5y)

\frac{\partial}{\partial x} (x^{4} - 4 x^{5} y)

4 x^{3} - 20 y x^{4}

Solution steps

\frac{\partial}{\partial x} (x^{4} - 4 x^{5} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{4}) - \frac{\partial}{\partial x} (4 x^{5} y)

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

\frac{\partial}{\partial x} (4 x^{5} y) = 20 y x^{4}

= 4 x^{3} - 20 y x^{4}

x \to 0 lim (x^{4} cos (\frac{6}{x}))

\frac{e ^{- 4 s}}{s - 2}

\int \frac{x - 1}{x ^{2}} d x

\int \frac{9}{x ( x ^{4} + 2 )} d x

\frac{\partial}{\partial x} (x sin (x) + y sin (y))

What is (\partial)/(\partial x)(x^4-4x^5y) ?
The answer to (\partial)/(\partial x)(x^4-4x^5y) is 4x^3-20yx^4