What is the derivative of x(6^{-2x}) ?

The derivative of x(6^{-2x}) is -ln(6)*9^{-x}*2^{-2x+1}x+36^{-x}

What is the first derivative of x(6^{-2x}) ?

The first derivative of x(6^{-2x}) is -ln(6)*9^{-x}*2^{-2x+1}x+36^{-x}

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\frac{d}{d x} (x (6^{- 2 x}))

- ln (6) \cdot 9^{- x} \cdot 2^{- 2 x + 1} x + 3 6^{- x}

Solution steps

\frac{d}{d x} (x (6^{- 2 x}))

Simplify

x (6^{- 2 x}) : 3 6^{- x} x

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

Apply the Product Rule:

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

f = 3 6^{- x}, g = x

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

\frac{d}{d x} (3 6^{- x}) = - ln (6) \cdot 9^{- x} \cdot 2^{- 2 x + 1}

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

= (- ln (6) \cdot 9^{- x} \cdot 2^{- 2 x + 1}) x + 1 \cdot 3 6^{- x}

Simplify

= - ln (6) \cdot 9^{- x} \cdot 2^{- 2 x + 1} x + 3 6^{- x}

e^{x^{4}}, 3

\int_{- π}^{π} x^{3} sin (n x) d x

7 - x - x^{2}

\frac{d}{d x} (\frac{x}{5 + x ^{2}})

y^{^{''}} + 9 y = 4 tan (3 x)

What is the derivative of x(6^{-2x}) ?
The derivative of x(6^{-2x}) is -ln(6)*9^{-x}*2^{-2x+1}x+36^{-x}
What is the first derivative of x(6^{-2x}) ?
The first derivative of x(6^{-2x}) is -ln(6)*9^{-x}*2^{-2x+1}x+36^{-x}