What is the derivative of 7^{3^{x^2}} ?

The derivative of 7^{3^{x^2}} is 2ln(7)ln(3)*7^{3^{x^2}}*3^{x^2}x

What is the first derivative of 7^{3^{x^2}} ?

The first derivative of 7^{3^{x^2}} is 2ln(7)ln(3)*7^{3^{x^2}}*3^{x^2}x

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\frac{d}{d x} (7^{3^{x^{2}}})

2 ln (7) ln (3) \cdot 7^{3^{x^{2}}} \cdot 3^{x^{2}} x

Solution steps

\frac{d}{d x} (7^{3^{x^{2}}})

Apply exponent rule:

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

7^{3^{x^{2}}} = e^{3^{x^{2}} l n (7)}

= \frac{d}{d x} (e^{3^{x^{2}} l n (7)})

Apply the chain rule:

e^{3^{x^{2}} l n (7)} \frac{d}{d x} (3^{x^{2}} ln (7))

= e^{3^{x^{2}} l n (7)} \frac{d}{d x} (3^{x^{2}} ln (7))

\frac{d}{d x} (3^{x^{2}} ln (7)) = 2 ln (7) ln (3) \cdot 3^{x^{2}} x

= e^{3^{x^{2}} l n (7)} \cdot 2 ln (7) ln (3) \cdot 3^{x^{2}} x

e^{3^{x^{2}} l n (7)} = 7^{3^{x^{2}}}

= 2 ln (7) ln (3) \cdot 7^{3^{x^{2}}} \cdot 3^{x^{2}} x

4 + 7 cos (5 t)

\int \frac{6}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d y}{( 5 - 3 y ) ^{2}} = \frac{d x}{2 ( 4 - x ) ^{2}}

f^{^{'}} (x) = x e^{- x^{2}}

e^{- 5 t} \cdot e^{25 t} cos (20 t)

What is the derivative of 7^{3^{x^2}} ?
The derivative of 7^{3^{x^2}} is 2ln(7)ln(3)*7^{3^{x^2}}*3^{x^2}x
What is the first derivative of 7^{3^{x^2}} ?
The first derivative of 7^{3^{x^2}} is 2ln(7)ln(3)*7^{3^{x^2}}*3^{x^2}x