What is (\partial)/(\partial x)(y(x^2+y)^6) ?

The answer to (\partial)/(\partial x)(y(x^2+y)^6) is 12yx(x^2+y)^5

Popular >

(\partial)/(\partial x)(y(x^2+y)^6)

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

12 y x (x^{2} + y)^{5}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} ((x^{2} + y)^{6})

Apply the chain rule:

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

= 6 (x^{2} + y)^{5} \frac{\partial}{\partial x} (x^{2} + y)

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

= y \cdot 6 (x^{2} + y)^{5} \cdot 2 x

Simplify

= 12 y x (x^{2} + y)^{5}

x \to - 1 lim (x + 5)

\frac{\partial}{\partial x} (4 x + 2 y)

\frac{d}{d x} (\frac{2}{5 x - 1})

\frac{4}{s}

\int (x + 5)^{9} d x

What is (\partial)/(\partial x)(y(x^2+y)^6) ?
The answer to (\partial)/(\partial x)(y(x^2+y)^6) is 12yx(x^2+y)^5