What is the derivative of 5^{3^{x^2}} ?

The derivative of 5^{3^{x^2}} is 2ln(5)ln(3)*5^{3^{x^2}}*3^{x^2}x

What is the first derivative of 5^{3^{x^2}} ?

The first derivative of 5^{3^{x^2}} is 2ln(5)ln(3)*5^{3^{x^2}}*3^{x^2}x

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derivative of

5^{3^{x^{2}}}

2 ln (5) ln (3) \cdot 5^{3^{x^{2}}} \cdot 3^{x^{2}} x

Solution steps

\frac{d}{d x} (5^{3^{x^{2}}})

Apply exponent rule:

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

5^{3^{x^{2}}} = e^{3^{x^{2}} l n (5)}

= \frac{d}{d x} (e^{3^{x^{2}} l n (5)})

Apply the chain rule:

e^{3^{x^{2}} l n (5)} \frac{d}{d x} (3^{x^{2}} ln (5))

= e^{3^{x^{2}} l n (5)} \frac{d}{d x} (3^{x^{2}} ln (5))

\frac{d}{d x} (3^{x^{2}} ln (5)) = 2 ln (5) ln (3) \cdot 3^{x^{2}} x

= e^{3^{x^{2}} l n (5)} \cdot 2 ln (5) ln (3) \cdot 3^{x^{2}} x

e^{3^{x^{2}} l n (5)} = 5^{3^{x^{2}}}

= 2 ln (5) ln (3) \cdot 5^{3^{x^{2}}} \cdot 3^{x^{2}} x

What is the derivative of 5^{3^{x^2}} ?
The derivative of 5^{3^{x^2}} is 2ln(5)ln(3)*5^{3^{x^2}}*3^{x^2}x
What is the first derivative of 5^{3^{x^2}} ?
The first derivative of 5^{3^{x^2}} is 2ln(5)ln(3)*5^{3^{x^2}}*3^{x^2}x