What is the derivative of (x-42^2-3xln((x-100)^2)) ?

The derivative of (x-42^2-3xln((x-100)^2)) is (2x^2-206x-6xln(x-100)+600ln(x-100))/(x-100)-84

What is the first derivative of (x-42^2-3xln((x-100)^2)) ?

The first derivative of (x-42^2-3xln((x-100)^2)) is (2x^2-206x-6xln(x-100)+600ln(x-100))/(x-100)-84

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\frac{d}{d x} ((x - 42)^{2} - 3 x ln ((x - 100)^{2}))

\frac{2 x ^{2} - 206 x - 6 x ln ( x - 100 ) + 600 ln ( x - 100 )}{x - 100} - 84

Solution steps

\frac{d}{d x} ((x - 42)^{2} - 3 x ln ((x - 100)^{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} ((x - 42)^{2}) - \frac{d}{d x} (3 x ln ((x - 100)^{2}))

\frac{d}{d x} ((x - 42)^{2}) = 2 (x - 42)

\frac{d}{d x} (3 x ln ((x - 100)^{2})) = 3 (2 ln (x - 100) + \frac{2 x}{x - 100})

= 2 (x - 42) - 3 (2 ln (x - 100) + \frac{2 x}{x - 100})

Simplify

2 (x - 42) - 3 (2 ln (x - 100) + \frac{2 x}{x - 100}) : \frac{2 x ^{2} - 206 x - 6 x ln ( x - 100 ) + 600 ln ( x - 100 )}{x - 100} - 84

= \frac{2 x ^{2} - 206 x - 6 x ln ( x - 100 ) + 600 ln ( x - 100 )}{x - 100} - 84

(e^{x} y) d y = (e^{- y} + e^{- 2 x - y}) d x

ln (t)

x \to 5 lim (2 x^{2} - 3 x + 4)

- \frac{7 x}{y}

\frac{1}{2} (e^{x} + e^{- x})

What is the derivative of (x-42^2-3xln((x-100)^2)) ?
The derivative of (x-42^2-3xln((x-100)^2)) is (2x^2-206x-6xln(x-100)+600ln(x-100))/(x-100)-84
What is the first derivative of (x-42^2-3xln((x-100)^2)) ?
The first derivative of (x-42^2-3xln((x-100)^2)) is (2x^2-206x-6xln(x-100)+600ln(x-100))/(x-100)-84