What is (\partial)/(\partial x)((x^3+y^3)^{10}) ?

The answer to (\partial)/(\partial x)((x^3+y^3)^{10}) is 30x^2(x^3+y^3)^9

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(\partial)/(\partial x)((x^3+y^3)^{10})

\frac{\partial}{\partial x} ((x^{3} + y^{3})^{10})

30 x^{2} (x^{3} + y^{3})^{9}

Solution steps

\frac{\partial}{\partial x} ((x^{3} + y^{3})^{10})

Treat

y

as a constant

Apply the chain rule:

10 (x^{3} + y^{3})^{9} \frac{\partial}{\partial x} (x^{3} + y^{3})

= 10 (x^{3} + y^{3})^{9} \frac{\partial}{\partial x} (x^{3} + y^{3})

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

= 10 (x^{3} + y^{3})^{9} \cdot 3 x^{2}

Simplify

= 30 x^{2} (x^{3} + y^{3})^{9}

\int \frac{5 - x ^{2}}{3 x ^{3} + x} d x

f (x) = x e^{3 x}

\frac{\partial}{\partial x} (tan (6 + 2 x^{2} y^{4} z^{2}))

\int 9 csc^{2} (x) d x

\int_{2}^{5} x d x

What is (\partial)/(\partial x)((x^3+y^3)^{10}) ?
The answer to (\partial)/(\partial x)((x^3+y^3)^{10}) is 30x^2(x^3+y^3)^9