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

The derivative of x^7ln(8x) is 7x^6ln(8x)+x^6

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

The first derivative of x^7ln(8x) is 7x^6ln(8x)+x^6

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

7 x^{6} ln (8 x) + x^{6}

Solution steps

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

Apply the Product Rule:

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

f = x^{7}, g = ln (8 x)

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (ln (8 x)) = \frac{1}{x}

= 7 x^{6} ln (8 x) + \frac{1}{x} x^{7}

\frac{1}{x} x^{7} = x^{6}

= 7 x^{6} ln (8 x) + x^{6}

\frac{d}{d x} (\frac{tan ( x )}{x ^{2}})

f (x) = \frac{4 x}{x + 3}, (1, 1)

\frac{d}{d θ} (cos (θ) - θ sin (θ))

9 x^{2}, 8 x^{4} - 8 x^{2}

\frac{d y}{d x} + 2 x^{2} = 0

What is the derivative of x^7ln(8x) ?
The derivative of x^7ln(8x) is 7x^6ln(8x)+x^6
What is the first derivative of x^7ln(8x) ?
The first derivative of x^7ln(8x) is 7x^6ln(8x)+x^6