What is the derivative of 3^{x^2-2x+1} ?

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

What is the first derivative of 3^{x^2-2x+1} ?

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

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derivative of

3^{x^{2} - 2 x + 1}

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

Solution steps

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

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{(x^{2} - 2 x + 1) l n (3)})

Apply the chain rule:

e^{(x^{2} - 2 x + 1) l n (3)} \frac{d}{d x} ((x^{2} - 2 x + 1) ln (3))

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

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

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

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

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

\int y^{2} e^{- y} d y

y = \frac{10}{x}

\frac{d}{d x} (tan (\frac{x}{2}) - cot (\frac{x}{2}))

\int (2 x - 3) (4 x^{2} + 1) d x

\frac{d}{d x} (\frac{5 x}{x - 2})

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