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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\frac{d}{d x} (\frac{2 x + 1}{x + 5} (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}}

t^{2} y^{^{''}} + 19 t y^{^{'}} + 117 y = 0

- 10 x

\frac{d}{d x} (cot (f (x)))

\int 7 x e^{8 x} d x

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

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)