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Popular >

derivative of x(8^{-2x})

Solution

derivative of

x (8^{- 2 x})

Solution

- 3 ln (2) \cdot 2^{- 6 x + 1} x + 6 4^{- x}

Solution steps

\frac{d}{d x} (x \cdot 8^{- 2 x})

Simplify

x \cdot 8^{- 2 x} : 6 4^{- x} x

= \frac{d}{d x} (6 4^{- x} x)

Apply the Product Rule:

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

f = 6 4^{- x}, g = x

= \frac{d}{d x} (6 4^{- x}) x + \frac{d x}{d x} 6 4^{- x}

\frac{d}{d x} (6 4^{- x}) = - 3 ln (2) \cdot 2^{- 6 x + 1}

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

= (- 3 ln (2) \cdot 2^{- 6 x + 1}) x + 1 \cdot 6 4^{- x}

Simplify

= - 3 ln (2) \cdot 2^{- 6 x + 1} x + 6 4^{- x}

Popular Examples

laplacetransform 3/2 sin(2t)laplace transform

\frac{3}{2} sin (2 t)

limit as x approaches 3 of 1/(x-3)

x \to 3 lim (\frac{1}{x - 3})

f(x)=cos^2(2-x^2)

f (x) = cos^{2} (2 - x^{2})

integral of 1/(a^2+b^2x^2)

\int \frac{1}{a ^{2} + b ^{2} x ^{2}} d x

integral from 0 to 8 of 1/(sqrt(1+x))

\int_{0}^{8} \frac{1}{1 + x} d x

Frequently Asked Questions (FAQ)

What is the derivative of x(8^{-2x}) ?
The derivative of x(8^{-2x}) is -3ln(2)*2^{-6x+1}x+64^{-x}
What is the first derivative of x(8^{-2x}) ?
The first derivative of x(8^{-2x}) is -3ln(2)*2^{-6x+1}x+64^{-x}