What is the derivative of 2^{3x-2x^2} ?

The derivative of 2^{3x-2x^2} is ln(2)*2^{3x-2x^2}(3-4x)

What is the first derivative of 2^{3x-2x^2} ?

The first derivative of 2^{3x-2x^2} is ln(2)*2^{3x-2x^2}(3-4x)

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

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{3 x - 2 x^{2}} = e^{(3 x - 2 x^{2}) l n (2)}

= \frac{d}{d x} (e^{(3 x - 2 x^{2}) l n (2)})

Apply the chain rule:

e^{(3 x - 2 x^{2}) l n (2)} \frac{d}{d x} ((3 x - 2 x^{2}) ln (2))

= e^{(3 x - 2 x^{2}) l n (2)} \frac{d}{d x} ((3 x - 2 x^{2}) ln (2))

\frac{d}{d x} ((3 x - 2 x^{2}) ln (2)) = ln (2) (3 - 4 x)

= e^{(3 x - 2 x^{2}) l n (2)} ln (2) (3 - 4 x)

e^{(3 x - 2 x^{2}) l n (2)} = 2^{3 x - 2 x^{2}}

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

f (x) = 1 - \frac{1}{x}

y^{2} = x + 10, y^{2} = 8 - x

\frac{\partial}{\partial x} (\frac{1}{( x + y ) ^{2}})

x \to 1 lim (\frac{1}{1 + x ^{2}})

- 4 x^{2} + 9, x + 7, 0

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