What is the derivative of (2^{3x}/(ln(3))) ?

The derivative of (2^{3x}/(ln(3))) is (3ln(2)*8^x)/(ln(3))

What is the first derivative of (2^{3x}/(ln(3))) ?

The first derivative of (2^{3x}/(ln(3))) is (3ln(2)*8^x)/(ln(3))

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\frac{d}{d x} (\frac{2 ^{3 x}}{ln ( 3 )})

\frac{3 ln ( 2 ) \cdot 8 ^{x}}{ln ( 3 )}

Solution steps

\frac{d}{d x} (\frac{2 ^{3 x}}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (2^{3 x})

Apply exponent rule:

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

2^{3 x} = e^{3 x l n (2)}

= \frac{1}{ln ( 3 )} \frac{d}{d x} (e^{3 x l n (2)})

Apply the chain rule:

e^{3 x l n (2)} \frac{d}{d x} (3 x ln (2))

= e^{3 x l n (2)} \frac{d}{d x} (3 x ln (2))

\frac{d}{d x} (3 x ln (2)) = 3 ln (2)

= \frac{1}{ln ( 3 )} e^{3 x l n (2)} \cdot 3 ln (2)

Simplify

\frac{1}{ln ( 3 )} e^{3 x l n (2)} \cdot 3 ln (2) : \frac{3 ln ( 2 ) \cdot 8 ^{x}}{ln ( 3 )}

= \frac{3 ln ( 2 ) \cdot 8 ^{x}}{ln ( 3 )}

\int sin (5 x - 3) d x

f (x) = (x^{2}) sin (x - 2)

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

\int (1 - x^{3})^{2} x^{2} d x

\int_{- 1}^{1} (y^{2} - 2) - e^{y} d y

What is the derivative of (2^{3x}/(ln(3))) ?
The derivative of (2^{3x}/(ln(3))) is (3ln(2)*8^x)/(ln(3))
What is the first derivative of (2^{3x}/(ln(3))) ?
The first derivative of (2^{3x}/(ln(3))) is (3ln(2)*8^x)/(ln(3))