What is the derivative of (x-42^2-6xln(x-100)) ?

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

What is the first derivative of (x-42^2-6xln(x-100)) ?

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

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\frac{d}{d x} ((x - 42)^{2} - 6 x ln (x - 100))

\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} - 6 x ln (x - 100))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} ((x - 42)^{2}) - \frac{d}{d x} (6 x ln (x - 100))

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

\frac{d}{d x} (6 x ln (x - 100)) = 6 (ln (x - 100) + \frac{x}{x - 100})

= 2 (x - 42) - 6 (ln (x - 100) + \frac{x}{x - 100})

Simplify

2 (x - 42) - 6 (ln (x - 100) + \frac{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

\frac{\partial}{\partial x} (\frac{y}{x} + e^{x y} + x y^{2})

x^{\frac{1}{9}}

\frac{d}{d x} (\frac{1}{lo g _{2} ( x )})

\frac{d}{d x} (\frac{1}{3} tan^{3} (x))

f (x) = \frac{x ^{2} + 4}{x ^{2} - 4}

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