What is the derivative of 3^{x^2-x+5} ?

The derivative of 3^{x^2-x+5} is ln(3)*3^{x^2-x+5}(2x-1)

What is the first derivative of 3^{x^2-x+5} ?

The first derivative of 3^{x^2-x+5} is ln(3)*3^{x^2-x+5}(2x-1)

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\frac{d}{d x} (3^{x^{2} - x + 5})

ln (3) \cdot 3^{x^{2} - x + 5} (2 x - 1)

Solution steps

\frac{d}{d x} (3^{x^{2} - x + 5})

Apply exponent rule:

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

3^{x^{2} - x + 5} = e^{(x^{2} - x + 5) l n (3)}

= \frac{d}{d x} (e^{(x^{2} - x + 5) l n (3)})

Apply the chain rule:

e^{(x^{2} - x + 5) l n (3)} \frac{d}{d x} ((x^{2} - x + 5) ln (3))

= e^{(x^{2} - x + 5) l n (3)} \frac{d}{d x} ((x^{2} - x + 5) ln (3))

\frac{d}{d x} ((x^{2} - x + 5) ln (3)) = ln (3) (2 x - 1)

= e^{(x^{2} - x + 5) l n (3)} ln (3) (2 x - 1)

e^{(x^{2} - x + 5) l n (3)} = 3^{x^{2} - x + 5}

= ln (3) \cdot 3^{x^{2} - x + 5} (2 x - 1)

What is the derivative of 3^{x^2-x+5} ?
The derivative of 3^{x^2-x+5} is ln(3)*3^{x^2-x+5}(2x-1)
What is the first derivative of 3^{x^2-x+5} ?
The first derivative of 3^{x^2-x+5} is ln(3)*3^{x^2-x+5}(2x-1)