What is (\partial)/(\partial x)(5*(x-4)*y^3) ?

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

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(\partial)/(\partial x)(5(x-4)y^3)

\frac{\partial}{\partial x} (5 \cdot (x - 4) \cdot y^{3})

5 y^{3}

Solution steps

\frac{\partial}{\partial x} (5 (x - 4) y^{3})

Treat

y

as a constant

Take the constant out:

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

= 5 y^{3} \frac{\partial}{\partial x} (x - 4)

Apply the Sum/Difference Rule:

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

= 5 y^{3} (\frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (4) = 0

= 5 y^{3} (1 - 0)

Simplify

= 5 y^{3}

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

\int \frac{3}{5 x ^{2} + 5} d x

(9 x + 0.8 x^{2} + 0.07 x^{3})^{^{'}}

y = cos (x)

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