What is (\partial)/(\partial x)(y^{3x}) ?

The answer to (\partial)/(\partial x)(y^{3x}) is 3y^{3x}ln(y)

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(\partial)/(\partial x)(y^{3x})

\frac{\partial}{\partial x} (y^{3 x})

3 y^{3 x} ln (y)

Solution steps

\frac{\partial}{\partial x} (y^{3 x})

Treat

y

as a constant

Apply exponent rule:

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

y^{3 x} = e^{3 x l n (y)}

= \frac{\partial}{\partial x} (e^{3 x l n (y)})

Apply the chain rule:

e^{3 x l n (y)} \frac{\partial}{\partial x} (3 x ln (y))

= e^{3 x l n (y)} \frac{\partial}{\partial x} (3 x ln (y))

\frac{\partial}{\partial x} (3 x ln (y)) = 3 ln (y)

= e^{3 x l n (y)} \cdot 3 ln (y)

e^{3 x l n (y)} = y^{3 x}

= 3 y^{3 x} ln (y)

f (x) = x + 2, x, x = 1, x = 3

\frac{d}{d x} (\frac{25}{x})

\int \frac{x}{x ^{2} + 5} d x

\frac{d y}{d x} = e^{4 x} + 7 y

\int \frac{7 x ^{3} + 3 x}{x - 1} d x

What is (\partial)/(\partial x)(y^{3x}) ?
The answer to (\partial)/(\partial x)(y^{3x}) is 3y^{3x}ln(y)