What is (\partial)/(\partial x)(5y^{4x}) ?

The answer to (\partial)/(\partial x)(5y^{4x}) is 20y^{4x}ln(y)

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(\partial)/(\partial x)(5y^{4x})

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

20 y^{4 x} ln (y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

y^{4 x} = e^{4 x l n (y)}

= 5 \frac{\partial}{\partial x} (e^{4 x l n (y)})

Apply the chain rule:

e^{4 x l n (y)} \frac{\partial}{\partial x} (4 x ln (y))

= e^{4 x l n (y)} \frac{\partial}{\partial x} (4 x ln (y))

\frac{\partial}{\partial x} (4 x ln (y)) = 4 ln (y)

= 5 e^{4 x l n (y)} \cdot 4 ln (y)

Simplify

5 e^{4 x l n (y)} \cdot 4 ln (y) : 20 y^{4 x} ln (y)

= 20 y^{4 x} ln (y)

What is (\partial)/(\partial x)(5y^{4x}) ?
The answer to (\partial)/(\partial x)(5y^{4x}) is 20y^{4x}ln(y)