What is (\partial)/(\partial x)(5x^2y^3+2x^2+7y) ?

The answer to (\partial)/(\partial x)(5x^2y^3+2x^2+7y) is 10xy^3+4x

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(\partial)/(\partial x)(5x^2y^3+2x^2+7y)

\frac{\partial}{\partial x} (5 x^{2} y^{3} + 2 x^{2} + 7 y)

10 x y^{3} + 4 x

Solution steps

\frac{\partial}{\partial x} (5 x^{2} y^{3} + 2 x^{2} + 7 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{2} y^{3}) + \frac{\partial}{\partial x} (2 x^{2}) + \frac{\partial}{\partial x} (7 y)

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

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

\frac{\partial}{\partial x} (7 y) = 0

= 10 y^{3} x + 4 x + 0

Simplify

= 10 x y^{3} + 4 x

f (x) = e^{- x}, 5

y = ln (5 x \cdot (2 x^{3} - 4 x)^{5})

\int 1 + e^{x} sin (y) d x

\frac{d y}{d x} = \frac{( x + 3 y )}{( y - 3 x )}

y^{^{'}} = 3 x

What is (\partial)/(\partial x)(5x^2y^3+2x^2+7y) ?
The answer to (\partial)/(\partial x)(5x^2y^3+2x^2+7y) is 10xy^3+4x