What is the derivative of x^8ln(x) ?

The derivative of x^8ln(x) is 8x^7ln(x)+x^7

What is the first derivative of x^8ln(x) ?

The first derivative of x^8ln(x) is 8x^7ln(x)+x^7

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derivative of

x^{8} ln (x)

8 x^{7} ln (x) + x^{7}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{8}, g = ln (x)

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

\frac{1}{x} x^{8} = x^{7}

= 8 x^{7} ln (x) + x^{7}

f (x) = e^{3 x}

f (x) = 3^{x l n (x)}

e^{4 t} sin (2 t)

\frac{d}{d y} (\frac{y}{t ^{2} + y ^{2}})

\frac{d r}{d t} + 2 t r - r = 0, r (0) = 6

What is the derivative of x^8ln(x) ?
The derivative of x^8ln(x) is 8x^7ln(x)+x^7
What is the first derivative of x^8ln(x) ?
The first derivative of x^8ln(x) is 8x^7ln(x)+x^7