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

The answer to (\partial)/(\partial x)(5y-x+y^2sin(y)) is -1

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

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

- 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 - 1 + 0

Simplify

= - 1

\frac{d y}{d x} = y^{3} x e^{x^{2}}

y^{^{''}} - 8 y = 0

e^{x + y}

\int_{1}^{4} 5 x + 3 x^{2} - 8 d x

\frac{d y}{d x} = - \frac{( 2 y ^{2} )}{x ^{2}}

What is (\partial)/(\partial x)(5y-x+y^2sin(y)) ?
The answer to (\partial)/(\partial x)(5y-x+y^2sin(y)) is -1