What is the derivative of (x-2^{4x}) ?

The derivative of (x-2^{4x}) is 4(ln(x-2)+x/(x-2))(x-2)^{4x}

What is the first derivative of (x-2^{4x}) ?

The first derivative of (x-2^{4x}) is 4(ln(x-2)+x/(x-2))(x-2)^{4x}

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\frac{d}{d x} ((x - 2)^{4 x})

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

Solution steps

\frac{d}{d x} ((x - 2)^{4 x})

Apply exponent rule:

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

(x - 2)^{4 x} = e^{4 x l n (x - 2)}

= \frac{d}{d x} (e^{4 x l n (x - 2)})

Apply the chain rule:

e^{4 x l n (x - 2)} \frac{d}{d x} (4 x ln (x - 2))

= e^{4 x l n (x - 2)} \frac{d}{d x} (4 x ln (x - 2))

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

= e^{4 x l n (x - 2)} \cdot 4 (ln (x - 2) + \frac{x}{x - 2})

e^{4 x l n (x - 2)} = (x - 2)^{4 x}

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

\int (tan (2 x))^{2} d x

\int_{0}^{\frac{1}{300}} 94 sin (225) d t

\int \frac{2}{t ^{3}} d t

x \to 0 lim (\frac{6 - 6 cos ( x )}{3})

\int \frac{e ^{- x} ( - 4 + 4 x ln ( x ) )}{2 x} d x

What is the derivative of (x-2^{4x}) ?
The derivative of (x-2^{4x}) is 4(ln(x-2)+x/(x-2))(x-2)^{4x}
What is the first derivative of (x-2^{4x}) ?
The first derivative of (x-2^{4x}) is 4(ln(x-2)+x/(x-2))(x-2)^{4x}