What is the derivative of (x+7)*ln(x) ?

The derivative of (x+7)*ln(x) is ln(x)+(x+7)/x

What is the first derivative of (x+7)*ln(x) ?

The first derivative of (x+7)*ln(x) is ln(x)+(x+7)/x

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derivative of

(x + 7) \cdot ln (x)

ln (x) + \frac{x + 7}{x}

Solution steps

\frac{d}{d x} ((x + 7) ln (x))

Apply the Product Rule:

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

f = x + 7, g = ln (x)

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

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

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

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

Simplify

1 \cdot ln (x) + \frac{1}{x} (x + 7) : ln (x) + \frac{x + 7}{x}

= ln (x) + \frac{x + 7}{x}

\frac{1}{ln ( x )}

x \to 3 lim (4 - x^{2})

\frac{d}{d x} (2 x + \frac{8}{x})

\frac{\partial}{\partial y} (x + 2 y - 22)

cos^{2} (3 x - 1)

What is the derivative of (x+7)*ln(x) ?
The derivative of (x+7)*ln(x) is ln(x)+(x+7)/x
What is the first derivative of (x+7)*ln(x) ?
The first derivative of (x+7)*ln(x) is ln(x)+(x+7)/x