What is the derivative of y=x^2ln(4x+3) ?

The derivative of y=x^2ln(4x+3) is 2xln(4x+3)+(4x^2)/(4x+3)

What is the first derivative of y=x^2ln(4x+3) ?

The first derivative of y=x^2ln(4x+3) is 2xln(4x+3)+(4x^2)/(4x+3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = x^{2} ln (4 x + 3)

2 x ln (4 x + 3) + \frac{4 x ^{2}}{4 x + 3}

Solution steps

\frac{d}{d x} (x^{2} ln (4 x + 3))

Apply the Product Rule:

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

f = x^{2}, g = ln (4 x + 3)

= \frac{d}{d x} (x^{2}) ln (4 x + 3) + \frac{d}{d x} (ln (4 x + 3)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (ln (4 x + 3)) = \frac{4}{4 x + 3}

= 2 x ln (4 x + 3) + \frac{4}{4 x + 3} x^{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x ln (4 x + 3) + \frac{4 x ^{2}}{4 x + 3}

\frac{d}{d x} ((x^{2})^{x})

\int (2 y) d y

\int \frac{( 5 x - 7 )}{( x ^{2} - x - 2 ) ( x - 3 )} d x

y^{^{'}} + x y = - x^{2}

y = (5 x - 4)^{5} (3 - x^{3})^{5}

What is the derivative of y=x^2ln(4x+3) ?
The derivative of y=x^2ln(4x+3) is 2xln(4x+3)+(4x^2)/(4x+3)
What is the first derivative of y=x^2ln(4x+3) ?
The first derivative of y=x^2ln(4x+3) is 2xln(4x+3)+(4x^2)/(4x+3)