What is the derivative of f(x)=(7^{-3x}) ?

The derivative of f(x)=(7^{-3x}) is -3ln(7)*343^{-x}

What is the first derivative of f(x)=(7^{-3x}) ?

The first derivative of f(x)=(7^{-3x}) is -3ln(7)*343^{-x}

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derivative of

f (x) = (7^{- 3 x})

- 3 ln (7) \cdot 34 3^{- x}

Solution steps

\frac{d}{d x} (7^{- 3 x})

Simplify

7^{- 3 x} : 34 3^{- x}

= \frac{d}{d x} (34 3^{- x})

Apply exponent rule:

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

34 3^{- x} = e^{(- x) l n (343)}

= \frac{d}{d x} (e^{(- x) l n (343)})

Apply the chain rule:

e^{(- x) l n (343)} \frac{d}{d x} ((- x) ln (343))

= e^{(- x) l n (343)} \frac{d}{d x} ((- x) ln (343))

\frac{d}{d x} ((- x) ln (343)) = - 3 ln (7)

= e^{(- x) l n (343)} (- 3 ln (7))

Simplify

e^{(- x) l n (343)} (- 3 ln (7)) : - 3 ln (7) \cdot 34 3^{- x}

= - 3 ln (7) \cdot 34 3^{- x}

\int (4 x^{2} - \frac{2}{x}) d x

f (x) = - x^{2} + 1

\int 1 + 4 x^{2} d x

\int x^{2} e^{\frac{x}{2}} d x

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

What is the derivative of f(x)=(7^{-3x}) ?
The derivative of f(x)=(7^{-3x}) is -3ln(7)*343^{-x}
What is the first derivative of f(x)=(7^{-3x}) ?
The first derivative of f(x)=(7^{-3x}) is -3ln(7)*343^{-x}