What is the derivative of y=9^{5^{x^2}} ?

The derivative of y=9^{5^{x^2}} is 4ln(3)ln(5)*9^{5^{x^2}}*5^{x^2}x

What is the first derivative of y=9^{5^{x^2}} ?

The first derivative of y=9^{5^{x^2}} is 4ln(3)ln(5)*9^{5^{x^2}}*5^{x^2}x

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derivative of

y = 9^{5^{x^{2}}}

4 ln (3) ln (5) \cdot 9^{5^{x^{2}}} \cdot 5^{x^{2}} x

Solution steps

\frac{d}{d x} (9^{5^{x^{2}}})

Apply exponent rule:

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

9^{5^{x^{2}}} = e^{5^{x^{2}} l n (9)}

= \frac{d}{d x} (e^{5^{x^{2}} l n (9)})

Apply the chain rule:

e^{5^{x^{2}} l n (9)} \frac{d}{d x} (5^{x^{2}} ln (9))

= e^{5^{x^{2}} l n (9)} \frac{d}{d x} (5^{x^{2}} ln (9))

\frac{d}{d x} (5^{x^{2}} ln (9)) = 4 ln (3) ln (5) \cdot 5^{x^{2}} x

= e^{5^{x^{2}} l n (9)} \cdot 4 ln (3) ln (5) \cdot 5^{x^{2}} x

e^{5^{x^{2}} l n (9)} = 9^{5^{x^{2}}}

= 4 ln (3) ln (5) \cdot 9^{5^{x^{2}}} \cdot 5^{x^{2}} x

What is the derivative of y=9^{5^{x^2}} ?
The derivative of y=9^{5^{x^2}} is 4ln(3)ln(5)*9^{5^{x^2}}*5^{x^2}x
What is the first derivative of y=9^{5^{x^2}} ?
The first derivative of y=9^{5^{x^2}} is 4ln(3)ln(5)*9^{5^{x^2}}*5^{x^2}x