What is the derivative of (6^x)^5 ?

The derivative of (6^x)^5 is 5ln(6)*7776^x

What is the first derivative of (6^x)^5 ?

The first derivative of (6^x)^5 is 5ln(6)*7776^x

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derivative of

(6^{x})^{5}

5 ln (6) \cdot 777 6^{x}

Solution steps

\frac{d}{d x} ((6^{x})^{5})

Simplify

(6^{x})^{5} : 777 6^{x}

= \frac{d}{d x} (777 6^{x})

Apply the derivative exponent rule:

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

= 777 6^{x} ln (7776)

Simplify

ln (7776) : 5 ln (6)

= 5 ln (6) \cdot 777 6^{x}

x \to 0 lim (e^{- 5 x})

e^{- t} e^{3 t}

y = x^{2} + 3.5 x + 4 π, at x = - 4

x \to 0 + lim (\frac{x ^{2} e ^{\frac{1}{x}}}{1 + x ^{2}})

y^{^{'}} = \frac{x + 3}{y + 8}

What is the derivative of (6^x)^5 ?
The derivative of (6^x)^5 is 5ln(6)*7776^x
What is the first derivative of (6^x)^5 ?
The first derivative of (6^x)^5 is 5ln(6)*7776^x