What is the derivative of y=10^{3x} ?

The derivative of y=10^{3x} is 3ln(10)*1000^x

What is the first derivative of y=10^{3x} ?

The first derivative of y=10^{3x} is 3ln(10)*1000^x

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derivative of

y = 1 0^{3 x}

3 ln (10) \cdot 100 0^{x}

Solution steps

\frac{d}{d x} (1 0^{3 x})

Simplify

1 0^{3 x} : 100 0^{x}

= \frac{d}{d x} (100 0^{x})

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= 100 0^{x} ln (1000)

Simplify

ln (1000) : 3 ln (10)

= 3 ln (10) \cdot 100 0^{x}

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What is the derivative of y=10^{3x} ?
The derivative of y=10^{3x} is 3ln(10)*1000^x
What is the first derivative of y=10^{3x} ?
The first derivative of y=10^{3x} is 3ln(10)*1000^x