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

The derivative of 5^{x^5} is ln(5)*5^{x^5+1}x^4

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

The first derivative of 5^{x^5} is ln(5)*5^{x^5+1}x^4

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derivative of

5^{x^{5}}

ln (5) \cdot 5^{x^{5} + 1} x^{4}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5} ln (5)) = 5 ln (5) x^{4}

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

Simplify

e^{x^{5} l n (5)} \cdot 5 ln (5) x^{4} : ln (5) \cdot 5^{x^{5} + 1} x^{4}

= ln (5) \cdot 5^{x^{5} + 1} x^{4}

\int \frac{1}{ln ( 2 x )} d x

2 y = 5 x, y = 3, 2 y + 2 x = 7

\int x (3^{x}) d x

\int (\frac{1}{- 0.4 t ^{3}}) d t

x \to 2 lim (3 (2 x + 5))

What is the derivative of 5^{x^5} ?
The derivative of 5^{x^5} is ln(5)*5^{x^5+1}x^4
What is the first derivative of 5^{x^5} ?
The first derivative of 5^{x^5} is ln(5)*5^{x^5+1}x^4