What is (\partial)/(\partial x)(x^4-y^3) ?

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

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(\partial)/(\partial x)(x^4-y^3)

\frac{\partial}{\partial x} (x^{4} - y^{3})

4 x^{3}

Solution steps

\frac{\partial}{\partial x} (x^{4} - y^{3})

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} (y^{3})

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

\frac{\partial}{\partial x} (y^{3}) = 0

= 4 x^{3} - 0

Simplify

= 4 x^{3}

(e^{y} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{6} e^{- x} d y = 0

\frac{d ^{2}}{d x ^{2}} (x^{2} + 12)

x^{3} + x^{2}, 2 x^{2} + 2 x

cos (w)

\frac{d}{d x} (- \frac{4 x}{( x - 2 ) ^{3}})

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