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Popular >

derivative of y=(x-2)^{4x}

Solution

derivative of

y = (x - 2)^{4 x}

Solution

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}

Graph

Popular Examples

integral of (x^3+3x^2-2x+1)/(x^4+5x^2+4)

\int \frac{x ^{3} + 3 x ^{2} - 2 x + 1}{x ^{4} + 5 x ^{2} + 4} d x

derivative of ((x^2-1^{3/2})/(3x^3))

\frac{d}{d x} \frac{( x ^{2} - 1 ) ^{\frac{3}{2}}}{3 x ^{3}}

limit as x approaches 9+of 2/(x-9)

x \to 9 + lim (\frac{2}{x - 9})

tangent of f(x)=(20x)/(x^2-5),(5,5)tangent of

f (x) = \frac{20 x}{x ^{2} - 5}, (5, 5)

limit as x approaches 0 of (ax^2+bx^3)/(cx^2+dx^3)

x \to 0 lim (\frac{a x ^{2} + b x ^{3}}{c x ^{2} + d x ^{3}})

Frequently Asked Questions (FAQ)

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