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

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

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

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

- y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

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

= 0 - y + 0

Simplify

= - y

\int (4 x - \frac{1}{2 x}) d x

\int \frac{1}{y ^{2} - 16} d y

y^{^{'}} = t^{\frac{1}{4}} - y

\int_{- 7}^{7} (49 - x^{2}) d x

\frac{d}{d x} (ln (\frac{x + 3}{e ^{3 x}}))

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