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Popular >

derivative of 9^{x^2-x}

Solution

\frac{d}{d x} (9^{x^{2} - x})

Solution

2 ln (3) \cdot 9^{x^{2} - x} (2 x - 1)

Solution steps

\frac{d}{d x} (9^{x^{2} - x})

Apply exponent rule:

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

9^{x^{2} - x} = e^{(x^{2} - x) l n (9)}

= \frac{d}{d x} (e^{(x^{2} - x) l n (9)})

Apply the chain rule:

e^{(x^{2} - x) l n (9)} \frac{d}{d x} ((x^{2} - x) ln (9))

= e^{(x^{2} - x) l n (9)} \frac{d}{d x} ((x^{2} - x) ln (9))

\frac{d}{d x} ((x^{2} - x) ln (9)) = 2 ln (3) (2 x - 1)

= e^{(x^{2} - x) l n (9)} \cdot 2 ln (3) (2 x - 1)

e^{(x^{2} - x) l n (9)} = 9^{x^{2} - x}

= 2 ln (3) \cdot 9^{x^{2} - x} (2 x - 1)

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Frequently Asked Questions (FAQ)

What is the derivative of 9^{x^2-x} ?
The derivative of 9^{x^2-x} is 2ln(3)*9^{x^2-x}(2x-1)
What is the first derivative of 9^{x^2-x} ?
The first derivative of 9^{x^2-x} is 2ln(3)*9^{x^2-x}(2x-1)