What is the derivative of 5^{7-x^2} ?

The derivative of 5^{7-x^2} is -2ln(5)*5^{7-x^2}x

What is the first derivative of 5^{7-x^2} ?

The first derivative of 5^{7-x^2} is -2ln(5)*5^{7-x^2}x

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derivative of

5^{7 - x^{2}}

- 2 ln (5) \cdot 5^{7 - x^{2}} x

Solution steps

\frac{d}{d x} (5^{7 - x^{2}})

Apply exponent rule:

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

5^{7 - x^{2}} = e^{(7 - x^{2}) l n (5)}

= \frac{d}{d x} (e^{(7 - x^{2}) l n (5)})

Apply the chain rule:

e^{(7 - x^{2}) l n (5)} \frac{d}{d x} ((7 - x^{2}) ln (5))

= e^{(7 - x^{2}) l n (5)} \frac{d}{d x} ((7 - x^{2}) ln (5))

\frac{d}{d x} ((7 - x^{2}) ln (5)) = - 2 ln (5) x

= e^{(7 - x^{2}) l n (5)} (- 2 ln (5) x)

Simplify

e^{(7 - x^{2}) l n (5)} (- 2 ln (5) x) : - 2 ln (5) \cdot 5^{7 - x^{2}} x

= - 2 ln (5) \cdot 5^{7 - x^{2}} x

8 t

x^{2} - 6 x, - x^{2} + 4 x

f (t) = 3 t^{2} - t

\int \frac{2 x ^{2} + x + 1}{x ^{3} + 2 x ^{2} + x} d x

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

What is the derivative of 5^{7-x^2} ?
The derivative of 5^{7-x^2} is -2ln(5)*5^{7-x^2}x
What is the first derivative of 5^{7-x^2} ?
The first derivative of 5^{7-x^2} is -2ln(5)*5^{7-x^2}x