What is the derivative of y=(8/x)^{5x} ?

The derivative of y=(8/x)^{5x} is 5(8/x)^{5x}(ln(8/x)-1)

What is the first derivative of y=(8/x)^{5x} ?

The first derivative of y=(8/x)^{5x} is 5(8/x)^{5x}(ln(8/x)-1)

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derivative of

y = (\frac{8}{x})^{5 x}

5 (\frac{8}{x})^{5 x} (ln (\frac{8}{x}) - 1)

Solution steps

\frac{d}{d x} ((\frac{8}{x})^{5 x})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x ln (\frac{8}{x})) = 5 (ln (\frac{8}{x}) - 1)

= e^{5 x l n (\frac{8}{x})} \cdot 5 (ln (\frac{8}{x}) - 1)

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

= 5 (\frac{8}{x})^{5 x} (ln (\frac{8}{x}) - 1)

\frac{d}{d x} (ln (x + x^{2} + 5))

\int_{1}^{3} \frac{1}{x ^{2} - 2 x + 5} d x

\int e^{i 7 x} cos (4 x) d x

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

\frac{( s - 1 )}{4 s ^{2} + s + 24}

What is the derivative of y=(8/x)^{5x} ?
The derivative of y=(8/x)^{5x} is 5(8/x)^{5x}(ln(8/x)-1)
What is the first derivative of y=(8/x)^{5x} ?
The first derivative of y=(8/x)^{5x} is 5(8/x)^{5x}(ln(8/x)-1)