What is (\partial)/(\partial x)(5^{8^{x^2}}) ?

The answer to (\partial)/(\partial x)(5^{8^{x^2}}) is 3ln(5)ln(2)*5^{8^{x^2}}*2^{3x^2+1}x

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(\partial)/(\partial x)(5^{8^{x^2}})

\frac{\partial}{\partial x} (5^{8^{x^{2}}})

3 ln (5) ln (2) \cdot 5^{8^{x^{2}}} \cdot 2^{3 x^{2} + 1} x

Solution steps

\frac{\partial}{\partial x} (5^{8^{x^{2}}})

Apply exponent rule:

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

5^{8^{x^{2}}} = e^{8^{x^{2}} l n (5)}

= \frac{\partial}{\partial x} (e^{8^{x^{2}} l n (5)})

Apply the chain rule:

e^{8^{x^{2}} l n (5)} \frac{\partial}{\partial x} (8^{x^{2}} ln (5))

= e^{8^{x^{2}} l n (5)} \frac{\partial}{\partial x} (8^{x^{2}} ln (5))

\frac{\partial}{\partial x} (8^{x^{2}} ln (5)) = 3 ln (5) ln (2) \cdot 2^{3 x^{2} + 1} x

= e^{8^{x^{2}} l n (5)} \cdot 3 ln (5) ln (2) \cdot 2^{3 x^{2} + 1} x

e^{8^{x^{2}} l n (5)} = 5^{8^{x^{2}}}

= 3 ln (5) ln (2) \cdot 5^{8^{x^{2}}} \cdot 2^{3 x^{2} + 1} x

\int (e^{x} + 1) \cdot (x - 4) d x

\frac{d y}{d x} - \frac{1}{x} y = 1 - \frac{1}{x}

f (x) = 25 - x^{2}, (5, 0)

\frac{x + 7}{3 x ^{2} e ^{x}}

What is (\partial)/(\partial x)(5^{8^{x^2}}) ?
The answer to (\partial)/(\partial x)(5^{8^{x^2}}) is 3ln(5)ln(2)*5^{8^{x^2}}*2^{3x^2+1}x