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

The derivative of (5x^3-1^3ln(x^2+1)) is 45x^2ln(x^2+1)(5x^3-1)^2+(2x(5x^3-1)^3)/(x^2+1)

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

The first derivative of (5x^3-1^3ln(x^2+1)) is 45x^2ln(x^2+1)(5x^3-1)^2+(2x(5x^3-1)^3)/(x^2+1)

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

45 x^{2} ln (x^{2} + 1) (5 x^{3} - 1)^{2} + \frac{2 x ( 5 x ^{3} - 1 ) ^{3}}{x ^{2} + 1}

Solution steps

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

Apply the Product Rule:

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

f = (5 x^{3} - 1)^{3}, g = ln (x^{2} + 1)

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

\frac{d}{d x} ((5 x^{3} - 1)^{3}) = 45 x^{2} (5 x^{3} - 1)^{2}

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

= 45 x^{2} (5 x^{3} - 1)^{2} ln (x^{2} + 1) + \frac{2 x}{x ^{2} + 1} (5 x^{3} - 1)^{3}

Multiply fractions:

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

= 45 x^{2} ln (x^{2} + 1) (5 x^{3} - 1)^{2} + \frac{2 x ( 5 x ^{3} - 1 ) ^{3}}{x ^{2} + 1}

\int 3 x sin (x) d x

x \to 0 lim (x^{6} cos (\frac{8}{x}))

f (x) = \frac{x ^{5}}{10} + \frac{1}{6 x ^{3}}

\int_{0}^{2} \frac{x ^{2}}{x + 1} d x

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

What is the derivative of (5x^3-1^3ln(x^2+1)) ?
The derivative of (5x^3-1^3ln(x^2+1)) is 45x^2ln(x^2+1)(5x^3-1)^2+(2x(5x^3-1)^3)/(x^2+1)
What is the first derivative of (5x^3-1^3ln(x^2+1)) ?
The first derivative of (5x^3-1^3ln(x^2+1)) is 45x^2ln(x^2+1)(5x^3-1)^2+(2x(5x^3-1)^3)/(x^2+1)