What is the derivative of xln(x^6) ?

The derivative of xln(x^6) is 6ln(x)+6

What is the first derivative of xln(x^6) ?

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

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\frac{d}{d x} (x ln (x^{6}))

6 ln (x) + 6

Solution steps

\frac{d}{d x} (x ln (x^{6}))

Apply the Product Rule:

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

f = x, g = ln (x^{6})

= \frac{d x}{d x} ln (x^{6}) + \frac{d}{d x} (ln (x^{6})) x

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot ln (x^{6}) + \frac{6}{x} x : 6 ln (x) + 6

= 6 ln (x) + 6

f (x) = 110 x - 16 x^{2}, at 3

7 x

\frac{d x}{d t} = (\frac{( e ^{t} x + 1 )}{1 - e ^{t}})

\int \frac{x - 3}{( x + 4 ) ( x + 5 )} d x

csc (θ)

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