What is the derivative of (3x+1((x^2+4))/((6x-5))) ?

The derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)

What is the first derivative of (3x+1((x^2+4))/((6x-5))) ?

The first derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

\frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

Apply the Product Rule:

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

f = 3 x + 1, g = \frac{x ^{2} + 4}{6 x - 5}

= \frac{d}{d x} (3 x + 1) \frac{x ^{2} + 4}{6 x - 5} + \frac{d}{d x} (\frac{x ^{2} + 4}{6 x - 5}) (3 x + 1)

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

\frac{d}{d x} (\frac{x ^{2} + 4}{6 x - 5}) = \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}}

= 3 \cdot \frac{x ^{2} + 4}{6 x - 5} + \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}} (3 x + 1)

Simplify

3 \cdot \frac{x ^{2} + 4}{6 x - 5} + \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}} (3 x + 1) : \frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

= \frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

\int \frac{sin ( 2 x )}{sin ( x )} d x

y = 2 csc (8 x^{3} - 8 x + 8)

\int_{0}^{1} 8 cos (4 x) d x

\int tan^{3} (x) sec^{5} (x) d x

\frac{\partial}{\partial x} (\frac{1 - ln ( x )}{x ^{2}})

What is the derivative of (3x+1((x^2+4))/((6x-5))) ?
The derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)
What is the first derivative of (3x+1((x^2+4))/((6x-5))) ?
The first derivative of (3x+1((x^2+4))/((6x-5))) is (36x^3-39x^2-10x-84)/((6x-5)^2)