What is (\partial)/(\partial x)(7x-5x^2y+8yz^2) ?

The answer to (\partial)/(\partial x)(7x-5x^2y+8yz^2) is -10xy+7

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(\partial)/(\partial x)(7x-5x^2y+8yz^2)

\frac{\partial}{\partial x} (7 x - 5 x^{2} y + 8 y z^{2})

- 10 x y + 7

Solution steps

\frac{\partial}{\partial x} (7 x - 5 x^{2} y + 8 y z^{2})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (7 x) - \frac{\partial}{\partial x} (5 x^{2} y) + \frac{\partial}{\partial x} (8 y z^{2})

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

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

\frac{\partial}{\partial x} (8 y z^{2}) = 0

= 7 - 10 y x + 0

Simplify

= - 10 x y + 7

\int \frac{x ^{3}}{x ^{2} + 100} d x

f (x) = - 4 sin (x) + 9 x

y = - arcsin (5 x^{2} + 4)

f (x) = 3^{2 x + 1}

\int_{1}^{4} e^{x} d x

What is (\partial)/(\partial x)(7x-5x^2y+8yz^2) ?
The answer to (\partial)/(\partial x)(7x-5x^2y+8yz^2) is -10xy+7