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Popular >

derivative of 3*10^{2x}

Solution

\frac{d}{d x} (3 \cdot 1 0^{2 x})

Solution

3 ln (10) \cdot 2 5^{x} \cdot 2^{2 x + 1}

Solution steps

\frac{d}{d x} (3 \cdot 1 0^{2 x})

Simplify

3 \cdot 1 0^{2 x} : 3 \cdot 10 0^{x}

= \frac{d}{d x} (3 \cdot 10 0^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (10 0^{x})

Apply the derivative exponent rule:

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

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

Simplify

3 \cdot 10 0^{x} ln (100) : 3 ln (10) \cdot 2 5^{x} \cdot 2^{2 x + 1}

= 3 ln (10) \cdot 2 5^{x} \cdot 2^{2 x + 1}

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\int t ln (t + 1) d t

(\partial)/(\partial x)(2(1+y)x)

\frac{\partial}{\partial x} (2 (1 + y) x)

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d/(dy)((y^3)/(27)+9/(4y))

\frac{d}{d y} (\frac{y ^{3}}{27} + \frac{9}{4 y})

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Frequently Asked Questions (FAQ)

What is the derivative of 3*10^{2x} ?
The derivative of 3*10^{2x} is 3ln(10)*25^x*2^{2x+1}
What is the first derivative of 3*10^{2x} ?
The first derivative of 3*10^{2x} is 3ln(10)*25^x*2^{2x+1}