What is the derivative of x(9^{-2x}) ?

The derivative of x(9^{-2x}) is -4ln(3)*81^{-x}x+81^{-x}

What is the first derivative of x(9^{-2x}) ?

The first derivative of x(9^{-2x}) is -4ln(3)*81^{-x}x+81^{-x}

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derivative of

x (9^{- 2 x})

- 4 ln (3) \cdot 8 1^{- x} x + 8 1^{- x}

Solution steps

\frac{d}{d x} (x \cdot 9^{- 2 x})

Simplify

x \cdot 9^{- 2 x} : 8 1^{- x} x

= \frac{d}{d x} (8 1^{- x} x)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 8 1^{- x}, g = x

= \frac{d}{d x} (8 1^{- x}) x + \frac{d x}{d x} 8 1^{- x}

\frac{d}{d x} (8 1^{- x}) = - 4 ln (3) \cdot 8 1^{- x}

\frac{d x}{d x} = 1

= (- 4 ln (3) \cdot 8 1^{- x}) x + 1 \cdot 8 1^{- x}

Simplify

= - 4 ln (3) \cdot 8 1^{- x} x + 8 1^{- x}

What is the derivative of x(9^{-2x}) ?
The derivative of x(9^{-2x}) is -4ln(3)*81^{-x}x+81^{-x}
What is the first derivative of x(9^{-2x}) ?
The first derivative of x(9^{-2x}) is -4ln(3)*81^{-x}x+81^{-x}