What is the derivative of 2^{(x^2-3x+8)} ?

The derivative of 2^{(x^2-3x+8)} is ln(2)*2^{x^2-3x+8}(2x-3)

What is the first derivative of 2^{(x^2-3x+8)} ?

The first derivative of 2^{(x^2-3x+8)} is ln(2)*2^{x^2-3x+8}(2x-3)

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derivative of

2^{(x^{2} - 3 x + 8)}

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

Solution steps

\frac{d}{d x} (2^{x^{2} - 3 x + 8})

Apply exponent rule:

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

2^{x^{2} - 3 x + 8} = e^{(x^{2} - 3 x + 8) l n (2)}

= \frac{d}{d x} (e^{(x^{2} - 3 x + 8) l n (2)})

Apply the chain rule:

e^{(x^{2} - 3 x + 8) l n (2)} \frac{d}{d x} ((x^{2} - 3 x + 8) ln (2))

= e^{(x^{2} - 3 x + 8) l n (2)} \frac{d}{d x} ((x^{2} - 3 x + 8) ln (2))

\frac{d}{d x} ((x^{2} - 3 x + 8) ln (2)) = ln (2) (2 x - 3)

= e^{(x^{2} - 3 x + 8) l n (2)} ln (2) (2 x - 3)

e^{(x^{2} - 3 x + 8) l n (2)} = 2^{x^{2} - 3 x + 8}

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

f (x) = 5 + 8 x, at x = 0

x \to \infty lim (x \cdot \frac{1}{x})

\frac{1}{120 x}

\int_{- 2}^{2} f (x) d x

\int x^{2} (3 + 4 x^{3})^{9} d x

What is the derivative of 2^{(x^2-3x+8)} ?
The derivative of 2^{(x^2-3x+8)} is ln(2)*2^{x^2-3x+8}(2x-3)
What is the first derivative of 2^{(x^2-3x+8)} ?
The first derivative of 2^{(x^2-3x+8)} is ln(2)*2^{x^2-3x+8}(2x-3)