What is the derivative of (x-2^{x+1}) ?

The derivative of (x-2^{x+1}) is (ln(x-2)+(x+1)/(x-2))(x-2)^{x+1}

What is the first derivative of (x-2^{x+1}) ?

The first derivative of (x-2^{x+1}) is (ln(x-2)+(x+1)/(x-2))(x-2)^{x+1}

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

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

(x - 2)^{x + 1} = e^{(x + 1) l n (x - 2)}

= \frac{d}{d x} (e^{(x + 1) l n (x - 2)})

Apply the chain rule:

e^{(x + 1) l n (x - 2)} \frac{d}{d x} ((x + 1) ln (x - 2))

= e^{(x + 1) l n (x - 2)} \frac{d}{d x} ((x + 1) ln (x - 2))

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

= e^{(x + 1) l n (x - 2)} (ln (x - 2) + \frac{x + 1}{x - 2})

e^{(x + 1) l n (x - 2)} = (x - 2)^{x + 1}

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

(y^{- 2})^{^{'}}

\frac{\partial}{\partial x} (x^{6} y - 2 x^{3} y^{2})

y = x + 4, y = x^{2} + x - 12

2 (x + 1), 3 (x + 1), x = 4

x^{3} + x + 3

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