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Popular >

derivative of x^3ln(1+x)

Solution

\frac{d}{d x} (x^{3} ln (1 + x))

Solution

3 x^{2} ln (1 + x) + \frac{x ^{3}}{1 + x}

Solution steps

\frac{d}{d x} (x^{3} ln (1 + x))

Apply the Product Rule:

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

f = x^{3}, g = ln (1 + x)

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

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

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

= 3 x^{2} ln (1 + x) + \frac{1}{1 + x} x^{3}

\frac{1}{1 + x} x^{3} = \frac{x ^{3}}{1 + x}

= 3 x^{2} ln (1 + x) + \frac{x ^{3}}{1 + x}

Graph

Popular Examples

integral from 1 to 3 of 11r^3ln(r)

\int_{1}^{3} 11 r^{3} ln (r) d r

y^{''}+25y=40sin(5t)

y^{^{''}} + 25 y = 40 sin (5 t)

(\partial)/(\partial y)(xy+y)

\frac{\partial}{\partial y} (x y + y)

laplacetransform 10e^{(-10t)}laplace transform

10 e^{(- 10 t)}

integral of e^{4x}x

\int e^{4 x} x d x

Frequently Asked Questions (FAQ)

What is the derivative of x^3ln(1+x) ?
The derivative of x^3ln(1+x) is 3x^2ln(1+x)+(x^3)/(1+x)
What is the first derivative of x^3ln(1+x) ?
The first derivative of x^3ln(1+x) is 3x^2ln(1+x)+(x^3)/(1+x)