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

The answer to (\partial)/(\partial x)((y-x^2)^2+x^5) is -4x(y-x^2)+5x^4

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

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

g (x) = \frac{1}{( 1 + 2 x ) ^{3}}

1 - cos (x)

\int_{- π}^{π} π sin^{2} (x) d x

n = 1 \sum \infty \frac{( ( - 2 ) ^{n - 1} )}{7 ^{n}}

\int_{0}^{1} \frac{- 4 y}{e ^{2 y}} d y

What is (\partial)/(\partial x)((y-x^2)^2+x^5) ?
The answer to (\partial)/(\partial x)((y-x^2)^2+x^5) is -4x(y-x^2)+5x^4