What is the derivative of y=4^{-x}sin(x) ?

The derivative of y=4^{-x}sin(x) is -ln(2)*2^{-2x+1}sin(x)+4^{-x}cos(x)

What is the first derivative of y=4^{-x}sin(x) ?

The first derivative of y=4^{-x}sin(x) is -ln(2)*2^{-2x+1}sin(x)+4^{-x}cos(x)

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derivative of

y = 4^{- x} sin (x)

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

Solution steps

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

Apply the Product Rule:

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

f = 4^{- x}, g = sin (x)

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

Simplify

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

\int \frac{9 - x ^{2}}{7 x ^{3} + x} d x

x \to 2 lim (\frac{x ^{7} - 128}{x - 2})

\frac{d}{d x} (e e^{x})

\int - 2 x y d x

\int y - 2 d y

What is the derivative of y=4^{-x}sin(x) ?
The derivative of y=4^{-x}sin(x) is -ln(2)*2^{-2x+1}sin(x)+4^{-x}cos(x)
What is the first derivative of y=4^{-x}sin(x) ?
The first derivative of y=4^{-x}sin(x) is -ln(2)*2^{-2x+1}sin(x)+4^{-x}cos(x)