What is the derivative of (2x+1)/(x+5)*(3x-1) ?

The derivative of (2x+1)/(x+5)*(3x-1) is (6x^2+60x+6)/((x+5)^2)

What is the first derivative of (2x+1)/(x+5)*(3x-1) ?

The first derivative of (2x+1)/(x+5)*(3x-1) is (6x^2+60x+6)/((x+5)^2)

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derivative of

\frac{2 x + 1}{x + 5} \cdot (3 x - 1)

\frac{6 x ^{2} + 60 x + 6}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 1}{x + 5} (3 x - 1))

Apply the Product Rule:

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

f = \frac{2 x + 1}{x + 5}, g = 3 x - 1

= \frac{d}{d x} (\frac{2 x + 1}{x + 5}) (3 x - 1) + \frac{d}{d x} (3 x - 1) \frac{2 x + 1}{x + 5}

\frac{d}{d x} (\frac{2 x + 1}{x + 5}) = \frac{9}{( x + 5 ) ^{2}}

\frac{d}{d x} (3 x - 1) = 3

= \frac{9}{( x + 5 ) ^{2}} (3 x - 1) + 3 \cdot \frac{2 x + 1}{x + 5}

Simplify

\frac{9}{( x + 5 ) ^{2}} (3 x - 1) + 3 \cdot \frac{2 x + 1}{x + 5} : \frac{6 x ^{2} + 60 x + 6}{( x + 5 ) ^{2}}

= \frac{6 x ^{2} + 60 x + 6}{( x + 5 ) ^{2}}

e^{16 x}

\frac{d}{d x} (ln (x^{2} + 3))

\int (1) d x

x \to c lim (4)

\int sec^{2} (x) + 5 d x

What is the derivative of (2x+1)/(x+5)*(3x-1) ?
The derivative of (2x+1)/(x+5)*(3x-1) is (6x^2+60x+6)/((x+5)^2)
What is the first derivative of (2x+1)/(x+5)*(3x-1) ?
The first derivative of (2x+1)/(x+5)*(3x-1) is (6x^2+60x+6)/((x+5)^2)