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Popular >

derivative of x(4^{-2x})

Solution

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

Solution

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

Solution steps

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

Simplify

x (4^{- 2 x}) : 1 6^{- x} x

= \frac{d}{d x} (1 6^{- x} x)

Apply the Product Rule:

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

f = 1 6^{- x}, g = x

= \frac{d}{d x} (1 6^{- x}) x + \frac{d x}{d x} 1 6^{- x}

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

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

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

Simplify

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

Popular Examples

derivative of \sqrt[3]{tan(5x})

integral of (27)/(1-cos(9x))

\int \frac{27}{1 - cos ( 9 x )} d x

(dy)/(dx)=(2+y^2)/(2xy)

\frac{d y}{d x} = \frac{2 + y ^{2}}{2 x y}

integral from 1 to 6 of 12x^3-9x^2+2

\int_{1}^{6} 12 x^{3} - 9 x^{2} + 2 d x

derivative of log_{2}(((3x+1)/(x^2+1)))

\frac{d}{d x} (lo g_{2} (\frac{( 3 x + 1 )}{x ^{2} + 1}))

Frequently Asked Questions (FAQ)

What is the derivative of x(4^{-2x}) ?
The derivative of x(4^{-2x}) is -ln(2)*2^{-4x+2}x+16^{-x}
What is the first derivative of x(4^{-2x}) ?
The first derivative of x(4^{-2x}) is -ln(2)*2^{-4x+2}x+16^{-x}