What is (\partial)/(\partial x)(10x^3+3x^2y-3y^5) ?

The answer to (\partial)/(\partial x)(10x^3+3x^2y-3y^5) is 30x^2+6xy

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(\partial)/(\partial x)(10x^3+3x^2y-3y^5)

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

30 x^{2} + 6 x y

Solution steps

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (10 x^{3}) + \frac{\partial}{\partial x} (3 x^{2} y) - \frac{\partial}{\partial x} (3 y^{5})

\frac{\partial}{\partial x} (10 x^{3}) = 30 x^{2}

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

\frac{\partial}{\partial x} (3 y^{5}) = 0

= 30 x^{2} + 6 y x - 0

Simplify

= 30 x^{2} + 6 x y

y^{^{''}} - 11 y^{^{'}} + 30 y = 20 e^{t}

\int_{0}^{2} (sin (x) + e^{x}) d x

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

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 6}{x})

\int \frac{1}{x ^{3} + x ^{2}} d x

What is (\partial)/(\partial x)(10x^3+3x^2y-3y^5) ?
The answer to (\partial)/(\partial x)(10x^3+3x^2y-3y^5) is 30x^2+6xy