What is the derivative of (x-1(x+1)(ln(900)-ln(x))) ?

The derivative of (x-1(x+1)(ln(900)-ln(x))) is 4ln(30)x-2xln(x)-x+(x+1)/x-1

What is the first derivative of (x-1(x+1)(ln(900)-ln(x))) ?

The first derivative of (x-1(x+1)(ln(900)-ln(x))) is 4ln(30)x-2xln(x)-x+(x+1)/x-1

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\frac{d}{d x} ((x - 1) (x + 1) (ln (900) - ln (x)))

4 ln (30) x - 2 x ln (x) - x + \frac{x + 1}{x} - 1

Solution steps

\frac{d}{d x} ((x - 1) (x + 1) (ln (900) - ln (x)))

Simplify

(x - 1) (x + 1) (ln (900) - ln (x)) : (x - 1) (x + 1) (2 ln (30) - ln (x))

= \frac{d}{d x} ((x - 1) (x + 1) (2 ln (30) - ln (x)))

Apply the Product Rule:

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

f = x - 1, g = (x + 1) (2 ln (30) - ln (x))

= \frac{d}{d x} (x - 1) (x + 1) (2 ln (30) - ln (x)) + \frac{d}{d x} ((x + 1) (2 ln (30) - ln (x))) (x - 1)

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

\frac{d}{d x} ((x + 1) (2 ln (30) - ln (x))) = 2 ln (30) - ln (x) - \frac{x + 1}{x}

= 1 \cdot (x + 1) (2 ln (30) - ln (x)) + (2 ln (30) - ln (x) - \frac{x + 1}{x}) (x - 1)

Simplify

1 \cdot (x + 1) (2 ln (30) - ln (x)) + (2 ln (30) - ln (x) - \frac{x + 1}{x}) (x - 1) : 4 ln (30) x - 2 x ln (x) - x + \frac{x + 1}{x} - 1

= 4 ln (30) x - 2 x ln (x) - x + \frac{x + 1}{x} - 1

\frac{1}{s ( s ^{2} + 9 )}

f (x) = 2 cos (x) + cos^{2} (x)

\frac{d}{d x} (7 e^{- 2 x})

\int \frac{1}{sin ^{2} ( x ) cos ^{2} ( x )} d x

\frac{8}{( 1 - x ) ^{2}}

What is the derivative of (x-1(x+1)(ln(900)-ln(x))) ?
The derivative of (x-1(x+1)(ln(900)-ln(x))) is 4ln(30)x-2xln(x)-x+(x+1)/x-1
What is the first derivative of (x-1(x+1)(ln(900)-ln(x))) ?
The first derivative of (x-1(x+1)(ln(900)-ln(x))) is 4ln(30)x-2xln(x)-x+(x+1)/x-1