What is (\partial)/(\partial x)((-x^4+7y^2+3y)^6) ?

The answer to (\partial)/(\partial x)((-x^4+7y^2+3y)^6) is -24x^3(-x^4+7y^2+3y)^5

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(\partial)/(\partial x)((-x^4+7y^2+3y)^6)

\frac{\partial}{\partial x} ((- x^{4} + 7 y^{2} + 3 y)^{6})

- 24 x^{3} (- x^{4} + 7 y^{2} + 3 y)^{5}

Solution steps

\frac{\partial}{\partial x} ((- x^{4} + 7 y^{2} + 3 y)^{6})

Treat

y

as a constant

Apply the chain rule:

6 (- x^{4} + 7 y^{2} + 3 y)^{5} \frac{\partial}{\partial x} (- x^{4} + 7 y^{2} + 3 y)

= 6 (- x^{4} + 7 y^{2} + 3 y)^{5} \frac{\partial}{\partial x} (- x^{4} + 7 y^{2} + 3 y)

\frac{\partial}{\partial x} (- x^{4} + 7 y^{2} + 3 y) = - 4 x^{3}

= 6 (- x^{4} + 7 y^{2} + 3 y)^{5} (- 4 x^{3})

Simplify

= - 24 x^{3} (- x^{4} + 7 y^{2} + 3 y)^{5}

\int 1 + \frac{1}{2 x} d x

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 2

\int_{1}^{3} e^{x} d x

18 + \frac{12}{( 0.0004 x ^{2} + 1 ) ^{2}}

\int_{3}^{6} \frac{x}{x ^{2} + 6 x + 13} d x

What is (\partial)/(\partial x)((-x^4+7y^2+3y)^6) ?
The answer to (\partial)/(\partial x)((-x^4+7y^2+3y)^6) is -24x^3(-x^4+7y^2+3y)^5