What is the derivative of 7^{x^2-x} ?

The derivative of 7^{x^2-x} is ln(7)*7^{x^2-x}(2x-1)

What is the first derivative of 7^{x^2-x} ?

The first derivative of 7^{x^2-x} is ln(7)*7^{x^2-x}(2x-1)

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derivative of

7^{x^{2} - x}

ln (7) \cdot 7^{x^{2} - x} (2 x - 1)

Solution steps

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

Apply exponent rule:

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

7^{x^{2} - x} = e^{(x^{2} - x) l n (7)}

= \frac{d}{d x} (e^{(x^{2} - x) l n (7)})

Apply the chain rule:

e^{(x^{2} - x) l n (7)} \frac{d}{d x} ((x^{2} - x) ln (7))

= e^{(x^{2} - x) l n (7)} \frac{d}{d x} ((x^{2} - x) ln (7))

\frac{d}{d x} ((x^{2} - x) ln (7)) = ln (7) (2 x - 1)

= e^{(x^{2} - x) l n (7)} ln (7) (2 x - 1)

e^{(x^{2} - x) l n (7)} = 7^{x^{2} - x}

= ln (7) \cdot 7^{x^{2} - x} (2 x - 1)

\int_{0}^{\frac{π}{2}} cos^{4} (2 x) d x

x \frac{d y}{d x} - y = 2 x^{2} y^{2}

sin (2) x^{3}

x \to 2 + lim (x - 2)

f (x) = arccsc (x)

What is the derivative of 7^{x^2-x} ?
The derivative of 7^{x^2-x} is ln(7)*7^{x^2-x}(2x-1)
What is the first derivative of 7^{x^2-x} ?
The first derivative of 7^{x^2-x} is ln(7)*7^{x^2-x}(2x-1)