What is the derivative of (x^3+32^{-7x}) ?

The derivative of (x^3+32^{-7x}) is -7ln(2)*128^{-x}(x^3+3)+3*128^{-x}x^2

What is the first derivative of (x^3+32^{-7x}) ?

The first derivative of (x^3+32^{-7x}) is -7ln(2)*128^{-x}(x^3+3)+3*128^{-x}x^2

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Popular >

\frac{d}{d x} ((x^{3} + 3) 2^{- 7 x})

- 7 ln (2) \cdot 12 8^{- x} (x^{3} + 3) + 3 \cdot 12 8^{- x} x^{2}

Solution steps

\frac{d}{d x} ((x^{3} + 3) \cdot 2^{- 7 x})

Simplify

(x^{3} + 3) \cdot 2^{- 7 x} : 12 8^{- x} (x^{3} + 3)

= \frac{d}{d x} (12 8^{- x} (x^{3} + 3))

Apply the Product Rule:

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

f = 12 8^{- x}, g = x^{3} + 3

= \frac{d}{d x} (12 8^{- x}) (x^{3} + 3) + \frac{d}{d x} (x^{3} + 3) 12 8^{- x}

\frac{d}{d x} (12 8^{- x}) = - 7 ln (2) \cdot 12 8^{- x}

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

= (- 7 ln (2) \cdot 12 8^{- x}) (x^{3} + 3) + 3 x^{2} \cdot 12 8^{- x}

Simplify

= - 7 ln (2) \cdot 12 8^{- x} (x^{3} + 3) + 3 \cdot 12 8^{- x} x^{2}

\frac{d}{d x} (24 x^{2} + 8 x - 5)

\frac{d}{d t} (2 t + 3)

\int_{5}^{9} \frac{1}{x ^{2} - 1} d x

3 2 + 2 x + x^{3}

n = 3 \sum \infty \frac{3}{4} \cdot \frac{1}{4 ^{n}}

What is the derivative of (x^3+32^{-7x}) ?
The derivative of (x^3+32^{-7x}) is -7ln(2)*128^{-x}(x^3+3)+3*128^{-x}x^2
What is the first derivative of (x^3+32^{-7x}) ?
The first derivative of (x^3+32^{-7x}) is -7ln(2)*128^{-x}(x^3+3)+3*128^{-x}x^2