What is the derivative of 4^{5x} ?

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

What is the first derivative of 4^{5x} ?

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

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\frac{d}{d x} (4^{5 x})

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

Solution steps

\frac{d}{d x} (4^{5 x})

Simplify

4^{5 x} : 102 4^{x}

= \frac{d}{d x} (102 4^{x})

Apply the derivative exponent rule:

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

= 102 4^{x} ln (1024)

Simplify

102 4^{x} ln (1024) : 5 ln (2) \cdot 2^{10 x + 1}

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

\int x (x + 2)^{5} d x

\frac{d}{d x} ((\frac{6}{7})^{\frac{2}{3}})

\int x csc (\frac{π - x ^{2}}{3}) d x

f (x) = 4 arcsin (x^{4})

\frac{d}{d x} (- x^{5} - \frac{x ^{3}}{6} + \frac{3}{x} - \frac{1}{x ^{2}})

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