What is the derivative of x+4ln(x+10)-ln(2x+1) ?

The derivative of x+4ln(x+10)-ln(2x+1) is (6x-16)/((x+10)(2x+1))+1

What is the first derivative of x+4ln(x+10)-ln(2x+1) ?

The first derivative of x+4ln(x+10)-ln(2x+1) is (6x-16)/((x+10)(2x+1))+1

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derivative of

x + 4 ln (x + 10) - ln (2 x + 1)

\frac{6 x - 16}{( x + 10 ) ( 2 x + 1 )} + 1

Solution steps

\frac{d}{d x} (x + 4 ln (x + 10) - ln (2 x + 1))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} + \frac{d}{d x} (4 ln (x + 10)) - \frac{d}{d x} (ln (2 x + 1))

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

\frac{d}{d x} (4 ln (x + 10)) = \frac{4}{x + 10}

\frac{d}{d x} (ln (2 x + 1)) = \frac{2}{2 x + 1}

= 1 + \frac{4}{x + 10} - \frac{2}{2 x + 1}

Combine the fractions

\frac{4}{x + 10} - \frac{2}{2 x + 1} : \frac{6 x - 16}{( x + 10 ) ( 2 x + 1 )}

= \frac{6 x - 16}{( x + 10 ) ( 2 x + 1 )} + 1

\frac{2}{( 3 s + 1 )}

\int_{- 2}^{2} \frac{e ^{x}}{e ^{x} - 1} d x

\frac{d}{d x} (x e^{x s i n (x)})

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\int \frac{x - 15}{x ^{2} ( x + 3 )} d x

What is the derivative of x+4ln(x+10)-ln(2x+1) ?
The derivative of x+4ln(x+10)-ln(2x+1) is (6x-16)/((x+10)(2x+1))+1
What is the first derivative of x+4ln(x+10)-ln(2x+1) ?
The first derivative of x+4ln(x+10)-ln(2x+1) is (6x-16)/((x+10)(2x+1))+1