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

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

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

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

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

ln^{2} (x + 1) + 2 ln (x + 1)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

y = x (x^{2} + 1)

f (y) = cos^{2} (y)

\int sec^{4} (5 x) tan^{3} (5 x) d x

f^{^{'}} (x) = \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + x}}}

\frac{x ^{3}}{1 - x ^{2}}

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