What is (\partial)/(\partial x)(y^{xz}+2(yz)^x) ?

The answer to (\partial)/(\partial x)(y^{xz}+2(yz)^x) is zy^{zx}ln(y)+2(yz)^xln(yz)

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(\partial)/(\partial x)(y^{xz}+2(yz)^x)

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

z y^{z x} ln (y) + 2 (yz)^{x} ln (yz)

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (y^{x z}) = z y^{z x} ln (y)

\frac{\partial}{\partial x} (2 (yz)^{x}) = 2 (yz)^{x} ln (yz)

= z y^{z x} ln (y) + 2 (yz)^{x} ln (yz)

\int \frac{tan ( ln ( y ) )}{y} d y

\int 120 x (2 x + 120)^{4} d x

2 x \frac{d y}{d x} = 10 x^{3} y^{5} + y

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

What is (\partial)/(\partial x)(y^{xz}+2(yz)^x) ?
The answer to (\partial)/(\partial x)(y^{xz}+2(yz)^x) is zy^{zx}ln(y)+2(yz)^xln(yz)