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Popular >

derivative of (1+x^2ln(1+x))

Solution

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

Solution

2 ln (1 + x) (1 + x) + 1 + x

Solution steps

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

Apply the Product Rule:

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

f = (1 + x)^{2}, g = ln (1 + x)

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

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

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

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

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

= 2 ln (1 + x) (1 + x) + 1 + x

Popular Examples

y^{10}y^'=13cos(pix)

y^{10} y^{^{'}} = 13 cos (π x)

integral of 7-3(1+x^2)^{-1}

\int 7 - 3 (1 + x^{2})^{- 1} d x

6x^{''}+1960x=0,x(0)=-3,x^'(0)=0

6 x^{^{''}} + 1960 x = 0, x (0) = - 3, x^{^{'}} (0) = 0

tangent of f(x)=(sqrt(3))^x,\at x=8 tangent of

f (x) = (3)^{x}, at x = 8

limit as x approaches 2 of 2^{c*x}

x \to 2 lim (2^{c \cdot x})

Frequently Asked Questions (FAQ)

What is the derivative of (1+x^2ln(1+x)) ?
The derivative of (1+x^2ln(1+x)) is 2ln(1+x)(1+x)+1+x
What is the first derivative of (1+x^2ln(1+x)) ?
The first derivative of (1+x^2ln(1+x)) is 2ln(1+x)(1+x)+1+x