What is the derivative of 7xln((16x)/(16x+1)) ?

The derivative of 7xln((16x)/(16x+1)) is 7(ln((16x)/(16x+1))+1/(16x+1))

What is the first derivative of 7xln((16x)/(16x+1)) ?

The first derivative of 7xln((16x)/(16x+1)) is 7(ln((16x)/(16x+1))+1/(16x+1))

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derivative of

7 x ln (\frac{16 x}{16 x + 1})

7 (ln (\frac{16 x}{16 x + 1}) + \frac{1}{16 x + 1})

Solution steps

\frac{d}{d x} (7 x ln (\frac{16 x}{16 x + 1}))

Take the constant out:

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

= 7 \frac{d}{d x} (x ln (\frac{16 x}{16 x + 1}))

Apply the Product Rule:

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

f = x, g = ln (\frac{16 x}{16 x + 1})

= 7 (\frac{d x}{d x} ln (\frac{16 x}{16 x + 1}) + \frac{d}{d x} (ln (\frac{16 x}{16 x + 1})) x)

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

\frac{d}{d x} (ln (\frac{16 x}{16 x + 1})) = \frac{1}{x ( 16 x + 1 )}

= 7 (1 \cdot ln (\frac{16 x}{16 x + 1}) + \frac{1}{x ( 16 x + 1 )} x)

Simplify

7 (1 \cdot ln (\frac{16 x}{16 x + 1}) + \frac{1}{x ( 16 x + 1 )} x) : 7 (ln (\frac{16 x}{16 x + 1}) + \frac{1}{16 x + 1})

= 7 (ln (\frac{16 x}{16 x + 1}) + \frac{1}{16 x + 1})

\frac{d y}{d x} = 2 x + 3 y

\int x \cdot e^{2 \cdot x} d x

\int \frac{1}{3 ( x + 1 )} d x

\int x cos (x) d x

\frac{d}{d x} (4 x - 10)

What is the derivative of 7xln((16x)/(16x+1)) ?
The derivative of 7xln((16x)/(16x+1)) is 7(ln((16x)/(16x+1))+1/(16x+1))
What is the first derivative of 7xln((16x)/(16x+1)) ?
The first derivative of 7xln((16x)/(16x+1)) is 7(ln((16x)/(16x+1))+1/(16x+1))