What is the derivative of f(x)=4x^{5x} ?

The derivative of f(x)=4x^{5x} is 20x^{5x}(ln(x)+1)

What is the first derivative of f(x)=4x^{5x} ?

The first derivative of f(x)=4x^{5x} is 20x^{5x}(ln(x)+1)

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derivative of

f (x) = 4 x^{5 x}

20 x^{5 x} (ln (x) + 1)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

= 4 \frac{d}{d x} (e^{5 x l n (x)})

Apply the chain rule:

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

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

\frac{d}{d x} (5 x ln (x)) = 5 (ln (x) + 1)

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

Simplify

4 e^{5 x l n (x)} \cdot 5 (ln (x) + 1) : 20 x^{5 x} (ln (x) + 1)

= 20 x^{5 x} (ln (x) + 1)

y^{^{'}} + y cos (x) = 2 cos (x), y (0) = 4

\int x^{3} e^{2 x^{2}} d x

\frac{d}{d x} (e^{s i n (x) + c o s (x)})

\frac{d}{d x} ((sin (20 x))^{3})

x + 3

What is the derivative of f(x)=4x^{5x} ?
The derivative of f(x)=4x^{5x} is 20x^{5x}(ln(x)+1)
What is the first derivative of f(x)=4x^{5x} ?
The first derivative of f(x)=4x^{5x} is 20x^{5x}(ln(x)+1)