What is (\partial)/(\partial x)((x^2y-y^3)^5) ?

The answer to (\partial)/(\partial x)((x^2y-y^3)^5) is 10xy(x^2y-y^3)^4

Popular >

(\partial)/(\partial x)((x^2y-y^3)^5)

\frac{\partial}{\partial x} ((x^{2} y - y^{3})^{5})

10 x y (x^{2} y - y^{3})^{4}

Solution steps

\frac{\partial}{\partial x} ((x^{2} y - y^{3})^{5})

Treat

y

as a constant

Apply the chain rule:

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

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

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

= 5 (x^{2} y - y^{3})^{4} \cdot 2 y x

Simplify

= 10 x y (x^{2} y - y^{3})^{4}

- \frac{e ^{(- 2 s)}}{( s ^{2} - 4 s + 4 )}

\int x^{5} e^{4 x} d x

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

\frac{d}{d x} (tan (x) + x sec^{2} (x))

sin (tan (x) + sec (x))

What is (\partial)/(\partial x)((x^2y-y^3)^5) ?
The answer to (\partial)/(\partial x)((x^2y-y^3)^5) is 10xy(x^2y-y^3)^4