What is the derivative of 5^{(6x^2-x+2}) ?

The derivative of 5^{(6x^2-x+2}) is ln(5)*5^{6x^2-x+2}(12x-1)

What is the first derivative of 5^{(6x^2-x+2}) ?

The first derivative of 5^{(6x^2-x+2}) is ln(5)*5^{6x^2-x+2}(12x-1)

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\frac{d}{d x} (5^{(6 x^{2} - x + 2)})

ln (5) \cdot 5^{6 x^{2} - x + 2} (12 x - 1)

Solution steps

\frac{d}{d x} (5^{(6 x^{2} - x + 2)})

Apply exponent rule:

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

5^{6 x^{2} - x + 2} = e^{(6 x^{2} - x + 2) l n (5)}

= \frac{d}{d x} (e^{(6 x^{2} - x + 2) l n (5)})

Apply the chain rule:

e^{(6 x^{2} - x + 2) l n (5)} \frac{d}{d x} ((6 x^{2} - x + 2) ln (5))

= e^{(6 x^{2} - x + 2) l n (5)} \frac{d}{d x} ((6 x^{2} - x + 2) ln (5))

\frac{d}{d x} ((6 x^{2} - x + 2) ln (5)) = ln (5) (12 x - 1)

= e^{(6 x^{2} - x + 2) l n (5)} ln (5) (12 x - 1)

e^{(6 x^{2} - x + 2) l n (5)} = 5^{6 x^{2} - x + 2}

= ln (5) \cdot 5^{6 x^{2} - x + 2} (12 x - 1)

\int - \frac{1}{2 x ^{\frac{1}{2}} - x + 1} d x

y = (x^{2} + 1)^{x}

\frac{d}{d x} (\frac{5}{x ^{7}})

- 3 e^{4 t}

\int_{1}^{3} \frac{e ^{x}}{e ^{x} - 1} d x

What is the derivative of 5^{(6x^2-x+2}) ?
The derivative of 5^{(6x^2-x+2}) is ln(5)*5^{6x^2-x+2}(12x-1)
What is the first derivative of 5^{(6x^2-x+2}) ?
The first derivative of 5^{(6x^2-x+2}) is ln(5)*5^{6x^2-x+2}(12x-1)