What is (\partial)/(\partial x)((1+x^2)^{zsin(y)}) ?

The answer to (\partial)/(\partial x)((1+x^2)^{zsin(y)}) is zsin(y)(1+x^2)^{zsin(y)-1}*2x

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(\partial)/(\partial x)((1+x^2)^{zsin(y)})

\frac{\partial}{\partial x} ((1 + x^{2})^{z s i n (y)})

z sin (y) (1 + x^{2})^{z s i n (y) - 1} \cdot 2 x

Solution steps

\frac{\partial}{\partial x} ((1 + x^{2})^{z s i n (y)})

Treat

z, y

as constants

Apply the chain rule:

z sin (y) (1 + x^{2})^{z s i n (y) - 1} \frac{\partial}{\partial x} (1 + x^{2})

= z sin (y) (1 + x^{2})^{z s i n (y) - 1} \frac{\partial}{\partial x} (1 + x^{2})

\frac{\partial}{\partial x} (1 + x^{2}) = 2 x

= z sin (y) (1 + x^{2})^{z s i n (y) - 1} \cdot 2 x

What is (\partial)/(\partial x)((1+x^2)^{zsin(y)}) ?
The answer to (\partial)/(\partial x)((1+x^2)^{zsin(y)}) is zsin(y)(1+x^2)^{zsin(y)-1}*2x