What is the derivative of y=-8xln(6x+5) ?

The derivative of y=-8xln(6x+5) is -8(ln(6x+5)+(6x)/(6x+5))

What is the first derivative of y=-8xln(6x+5) ?

The first derivative of y=-8xln(6x+5) is -8(ln(6x+5)+(6x)/(6x+5))

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derivative of

y = - 8 x ln (6 x + 5)

- 8 (ln (6 x + 5) + \frac{6 x}{6 x + 5})

Solution steps

\frac{d}{d x} (- 8 x ln (6 x + 5))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 8 \frac{d}{d x} (x ln (6 x + 5))

Apply the Product Rule:

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

f = x, g = ln (6 x + 5)

= - 8 (\frac{d x}{d x} ln (6 x + 5) + \frac{d}{d x} (ln (6 x + 5)) x)

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

\frac{d}{d x} (ln (6 x + 5)) = \frac{6}{6 x + 5}

= - 8 (1 \cdot ln (6 x + 5) + \frac{6}{6 x + 5} x)

Simplify

- 8 (1 \cdot ln (6 x + 5) + \frac{6}{6 x + 5} x) : - 8 (ln (6 x + 5) + \frac{6 x}{6 x + 5})

= - 8 (ln (6 x + 5) + \frac{6 x}{6 x + 5})

\int_{0}^{1} (x + 3) (x - 4) d x

y = (x^{3} - 16 x)^{12}, (4, 0)

\frac{d}{d y} (arctan (x + 2 y))

x \to 2 lim (20 - x^{2})

\frac{d}{d x} (x - 2)

What is the derivative of y=-8xln(6x+5) ?
The derivative of y=-8xln(6x+5) is -8(ln(6x+5)+(6x)/(6x+5))
What is the first derivative of y=-8xln(6x+5) ?
The first derivative of y=-8xln(6x+5) is -8(ln(6x+5)+(6x)/(6x+5))