What is the derivative of 6^{(4-3x}) ?

The derivative of 6^{(4-3x}) is -ln(6)*2^{4-3x}*3^{-3x+5}

What is the first derivative of 6^{(4-3x}) ?

The first derivative of 6^{(4-3x}) is -ln(6)*2^{4-3x}*3^{-3x+5}

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\frac{d}{d x} (6^{(4 - 3 x)})

- ln (6) \cdot 2^{4 - 3 x} \cdot 3^{- 3 x + 5}

Solution steps

\frac{d}{d x} (6^{(4 - 3 x)})

Apply exponent rule:

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

6^{4 - 3 x} = e^{(4 - 3 x) l n (6)}

= \frac{d}{d x} (e^{(4 - 3 x) l n (6)})

Apply the chain rule:

e^{(4 - 3 x) l n (6)} \frac{d}{d x} ((4 - 3 x) ln (6))

= e^{(4 - 3 x) l n (6)} \frac{d}{d x} ((4 - 3 x) ln (6))

\frac{d}{d x} ((4 - 3 x) ln (6)) = - 3 ln (6)

= e^{(4 - 3 x) l n (6)} (- 3 ln (6))

Simplify

e^{(4 - 3 x) l n (6)} (- 3 ln (6)) : - ln (6) \cdot 2^{4 - 3 x} \cdot 3^{- 3 x + 5}

= - ln (6) \cdot 2^{4 - 3 x} \cdot 3^{- 3 x + 5}

What is the derivative of 6^{(4-3x}) ?
The derivative of 6^{(4-3x}) is -ln(6)*2^{4-3x}*3^{-3x+5}
What is the first derivative of 6^{(4-3x}) ?
The first derivative of 6^{(4-3x}) is -ln(6)*2^{4-3x}*3^{-3x+5}