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Popular >

derivative of 5^{x-2}

Solution

\frac{d}{d x} (5^{x - 2})

Solution

ln (5) \cdot 5^{x - 2}

Solution steps

\frac{d}{d x} (5^{x - 2})

Apply exponent rule:

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

5^{x - 2} = e^{(x - 2) l n (5)}

= \frac{d}{d x} (e^{(x - 2) l n (5)})

Apply the chain rule:

e^{(x - 2) l n (5)} \frac{d}{d x} ((x - 2) ln (5))

= e^{(x - 2) l n (5)} \frac{d}{d x} ((x - 2) ln (5))

\frac{d}{d x} ((x - 2) ln (5)) = ln (5)

= e^{(x - 2) l n (5)} ln (5)

e^{(x - 2) l n (5)} = 5^{x - 2}

= ln (5) \cdot 5^{x - 2}

Popular Examples

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f (x) = 2 x^{3} + 9 x^{2} - 60 x + 4

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(\partial)/(\partial x)(2xy^3-4x^2y^2)

\frac{\partial}{\partial x} (2 x y^{3} - 4 x^{2} y^{2})

slope of x^{1/2}+y^{1/2}=4 slope

x^{\frac{1}{2}} + y^{\frac{1}{2}} = 4

Frequently Asked Questions (FAQ)

What is the derivative of 5^{x-2} ?
The derivative of 5^{x-2} is ln(5)*5^{x-2}
What is the first derivative of 5^{x-2} ?
The first derivative of 5^{x-2} is ln(5)*5^{x-2}