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

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

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

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

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derivative of

5^{x^{2}}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

= e^{x^{2} l n (5)} \cdot 2 ln (5) x

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

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

(1 - x^{3}) y^{^{'}} - 2 (1 + x) y = y^{\frac{5}{2}}

\int 8 + 6 x + 24 x^{2} d x

\frac{d}{d x} (\frac{9 e ^{x} x ^{\frac{7}{2}}}{2} + e^{x} x^{\frac{9}{2}})

\frac{\partial}{\partial x} (\frac{4 x + 9}{3 y + 1})

f (x) = 4 x^{2} + 5 x + 3

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