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}

\frac{d}{d x} (\frac{x}{x ^{2} + 49})

\int x^{- \frac{1}{7}} d x

\frac{1}{x + 4}

\int \frac{x ^{5}}{x ^{6} + 1} d x

\frac{d}{d x} (10 ln (x))

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}