What is the derivative of (50x^4/(2^x)) ?

The derivative of (50x^4/(2^x)) is 25(-ln(2)*2^{1-x}x^4+2^{-x+3}x^3)

What is the first derivative of (50x^4/(2^x)) ?

The first derivative of (50x^4/(2^x)) is 25(-ln(2)*2^{1-x}x^4+2^{-x+3}x^3)

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\frac{d}{d x} (\frac{50 x ^{4}}{2 ^{x}})

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

Solution steps

\frac{d}{d x} (\frac{50 x ^{4}}{2 ^{x}})

Simplify

\frac{50 x ^{4}}{2 ^{x}} : 25 \cdot 2^{1 - x} x^{4}

= \frac{d}{d x} (25 \cdot 2^{1 - x} x^{4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 25 \frac{d}{d x} (2^{1 - x} x^{4})

Apply the Product Rule:

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

f = 2^{1 - x}, g = x^{4}

= 25 (\frac{d}{d x} (2^{1 - x}) x^{4} + \frac{d}{d x} (x^{4}) 2^{1 - x})

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= 25 ((- ln (2) \cdot 2^{1 - x}) x^{4} + 4 x^{3} \cdot 2^{1 - x})

Simplify

25 ((- ln (2) \cdot 2^{1 - x}) x^{4} + 4 x^{3} \cdot 2^{1 - x}) : 25 (- ln (2) \cdot 2^{1 - x} x^{4} + 2^{- x + 3} x^{3})

= 25 (- ln (2) \cdot 2^{1 - x} x^{4} + 2^{- x + 3} x^{3})

\int_{0}^{6} 12 x - 3 x^{2} d x

f (x) = x^{3} - x, at x = - 1

x \to \infty lim (5^{x} + 5)

\frac{\partial}{\partial x} (x cos (x^{2} y))

What is the derivative of (50x^4/(2^x)) ?
The derivative of (50x^4/(2^x)) is 25(-ln(2)*2^{1-x}x^4+2^{-x+3}x^3)
What is the first derivative of (50x^4/(2^x)) ?
The first derivative of (50x^4/(2^x)) is 25(-ln(2)*2^{1-x}x^4+2^{-x+3}x^3)