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Popular >

derivative of ln(x^8y)

Solution

\frac{d}{d x} (ln (x^{8} y))

Solution

\frac{8 y + x \frac{d y}{d x}}{x y}

Solution steps

\frac{d}{d x} (ln (x^{8} y))

Apply the chain rule:

\frac{1}{x ^{8} y} \frac{d}{d x} (x^{8} y)

= \frac{1}{x ^{8} y} \frac{d}{d x} (x^{8} y)

\frac{d}{d x} (x^{8} y) = 8 x^{7} y + \frac{d y}{d x} x^{8}

= \frac{1}{x ^{8} y} (8 x^{7} y + \frac{d y}{d x} x^{8})

Simplify

\frac{1}{x ^{8} y} (8 x^{7} y + \frac{d y}{d x} x^{8}) : \frac{8 y + x \frac{d y}{d x}}{x y}

= \frac{8 y + x \frac{d y}{d x}}{x y}

Popular Examples

integral from 0 to 1 of xe^{5x}

\int_{0}^{1} x e^{5 x} d x

y^{''}-4y^'+4y=4-8t-(18te^{2t}+2e^{2t})

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 - 8 t - (18 t e^{2 t} + 2 e^{2 t})

integral of 2*x*ln(x)

\int 2 \cdot x \cdot ln (x) d x

(\partial)/(\partial y)(-1/2 x-3y+1)

\frac{\partial}{\partial y} (- \frac{1}{2} x - 3 y + 1)

integral of ucos(u)

\int u cos (u) d u

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^8y) ?
The derivative of ln(x^8y) is (8y+x\frac{dy)/(dx)}{xy}
What is the first derivative of ln(x^8y) ?
The first derivative of ln(x^8y) is (8y+x\frac{dy)/(dx)}{xy}