What is the derivative of 10^{2x-1} ?

The derivative of 10^{2x-1} is ln(10)*4^x*5^{2x-1}

What is the first derivative of 10^{2x-1} ?

The first derivative of 10^{2x-1} is ln(10)*4^x*5^{2x-1}

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\frac{d}{d x} (1 0^{2 x - 1})

ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

Solution steps

\frac{d}{d x} (1 0^{2 x - 1})

Apply exponent rule:

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

1 0^{2 x - 1} = e^{(2 x - 1) l n (10)}

= \frac{d}{d x} (e^{(2 x - 1) l n (10)})

Apply the chain rule:

e^{(2 x - 1) l n (10)} \frac{d}{d x} ((2 x - 1) ln (10))

= e^{(2 x - 1) l n (10)} \frac{d}{d x} ((2 x - 1) ln (10))

\frac{d}{d x} ((2 x - 1) ln (10)) = 2 ln (10)

= e^{(2 x - 1) l n (10)} \cdot 2 ln (10)

Simplify

e^{(2 x - 1) l n (10)} \cdot 2 ln (10) : ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

= ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

What is the derivative of 10^{2x-1} ?
The derivative of 10^{2x-1} is ln(10)*4^x*5^{2x-1}
What is the first derivative of 10^{2x-1} ?
The first derivative of 10^{2x-1} is ln(10)*4^x*5^{2x-1}