What is (\partial)/(\partial x)(-(5x^3+5xy^2)) ?

The answer to (\partial)/(\partial x)(-(5x^3+5xy^2)) is -15x^2-5y^2

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(\partial)/(\partial x)(-(5x^3+5xy^2))

\frac{\partial}{\partial x} (- (5 x^{3} + 5 x y^{2}))

- 15 x^{2} - 5 y^{2}

Solution steps

\frac{\partial}{\partial x} (- (5 x^{3} + 5 x y^{2}))

Simplify

- (5 x^{3} + 5 x y^{2}) : - 5 x^{3} - 5 x y^{2}

= \frac{\partial}{\partial x} (- 5 x^{3} - 5 x y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial x} (5 x^{3}) - \frac{\partial}{\partial x} (5 x y^{2})

\frac{\partial}{\partial x} (5 x^{3}) = 15 x^{2}

\frac{\partial}{\partial x} (5 x y^{2}) = 5 y^{2}

= - 15 x^{2} - 5 y^{2}

\frac{\partial}{\partial h} (x^{2} h)

\frac{1}{x + 2}

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

\int x^{8} e^{x} d x

(x + 2) \frac{d y}{d x} + y = ln (x), y (1) = 20

What is (\partial)/(\partial x)(-(5x^3+5xy^2)) ?
The answer to (\partial)/(\partial x)(-(5x^3+5xy^2)) is -15x^2-5y^2