What is the derivative of 5^{2x^2+x+1} ?

The derivative of 5^{2x^2+x+1} is ln(5)*5^{2x^2+x+1}(4x+1)

What is the first derivative of 5^{2x^2+x+1} ?

The first derivative of 5^{2x^2+x+1} is ln(5)*5^{2x^2+x+1}(4x+1)

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derivative of

5^{2 x^{2} + x + 1}

ln (5) \cdot 5^{2 x^{2} + x + 1} (4 x + 1)

Solution steps

\frac{d}{d x} (5^{2 x^{2} + x + 1})

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{(2 x^{2} + x + 1) l n (5)})

Apply the chain rule:

e^{(2 x^{2} + x + 1) l n (5)} \frac{d}{d x} ((2 x^{2} + x + 1) ln (5))

= e^{(2 x^{2} + x + 1) l n (5)} \frac{d}{d x} ((2 x^{2} + x + 1) ln (5))

\frac{d}{d x} ((2 x^{2} + x + 1) ln (5)) = ln (5) (4 x + 1)

= e^{(2 x^{2} + x + 1) l n (5)} ln (5) (4 x + 1)

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

= ln (5) \cdot 5^{2 x^{2} + x + 1} (4 x + 1)

(x^{2} + 3 x + 3)^{- 3}

\frac{e ^{x}}{( e ^{x} + 1 )}

sin^{3} (x) + cos^{2} (x)

y = (x + 1) (x + 2) (x - 3)

4 t^{2} - 15 t + 25

What is the derivative of 5^{2x^2+x+1} ?
The derivative of 5^{2x^2+x+1} is ln(5)*5^{2x^2+x+1}(4x+1)
What is the first derivative of 5^{2x^2+x+1} ?
The first derivative of 5^{2x^2+x+1} is ln(5)*5^{2x^2+x+1}(4x+1)