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

The answer to (\partial)/(\partial x)((x^5+y^3)^7) is 35x^4(x^5+y^3)^6

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

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

35 x^{4} (x^{5} + y^{3})^{6}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{5} + y^{3}) = 5 x^{4}

= 7 (x^{5} + y^{3})^{6} \cdot 5 x^{4}

Simplify

= 35 x^{4} (x^{5} + y^{3})^{6}

\int \frac{z}{( s ^{2} + z ^{2} ) ^{\frac{3}{2}}} d z

m (x) = \frac{- x ^{2} + 6 x - 8}{- x ^{2} + 6 x - 2}

y = - 5 - 6 x^{2}, (- 4, - 101)

p (t) = 5 e^{0.0278 t}

\frac{d}{d x} (\frac{1}{2} x^{2} + 1)

What is (\partial)/(\partial x)((x^5+y^3)^7) ?
The answer to (\partial)/(\partial x)((x^5+y^3)^7) is 35x^4(x^5+y^3)^6