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

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

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

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

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derivative of

x (7^{- 3 x})

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = 34 3^{- x}, g = x

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

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

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

= (- 3 ln (7) \cdot 34 3^{- x}) x + 1 \cdot 34 3^{- x}

Simplify

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

\frac{d}{d x} (\frac{2 x ^{2} + x - 3}{- 3 x ^{2} - 4 x + 2})

x \to 2 lim (16)

n = 1 \sum \infty 5 (4)^{n - 1}

cos (3 x)

\frac{d}{d x} (\frac{1.05}{1 + 100 e ^{- 0.285 x}})

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