What is the derivative of y=14^{-8/x} ?

The derivative of y=14^{-8/x} is (ln(14)*2^{(3x-8)/x}*7^{-8/x})/(x^2)

What is the first derivative of y=14^{-8/x} ?

The first derivative of y=14^{-8/x} is (ln(14)*2^{(3x-8)/x}*7^{-8/x})/(x^2)

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derivative of

y = 1 4^{- \frac{8}{x}}

\frac{ln ( 14 ) \cdot 2 ^{\frac{3 x - 8}{x}} \cdot 7 ^{- \frac{8}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (1 4^{- \frac{8}{x}})

Apply exponent rule:

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

1 4^{- \frac{8}{x}} = e^{(- \frac{8}{x}) l n (14)}

= \frac{d}{d x} (e^{(- \frac{8}{x}) l n (14)})

Apply the chain rule:

e^{(- \frac{8}{x}) l n (14)} \frac{d}{d x} ((- \frac{8}{x}) ln (14))

= e^{(- \frac{8}{x}) l n (14)} \frac{d}{d x} ((- \frac{8}{x}) ln (14))

\frac{d}{d x} ((- \frac{8}{x}) ln (14)) = \frac{8 ln ( 14 )}{x ^{2}}

= e^{(- \frac{8}{x}) l n (14)} \frac{8 ln ( 14 )}{x ^{2}}

Simplify

e^{(- \frac{8}{x}) l n (14)} \frac{8 ln ( 14 )}{x ^{2}} : \frac{ln ( 14 ) \cdot 2 ^{\frac{3 x - 8}{x}} \cdot 7 ^{- \frac{8}{x}}}{x ^{2}}

= \frac{ln ( 14 ) \cdot 2 ^{\frac{3 x - 8}{x}} \cdot 7 ^{- \frac{8}{x}}}{x ^{2}}

\frac{d}{d x} (20 + x)

\frac{\partial}{\partial x} ((x y - 3) e^{- x y})

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 x^{2} - 5 x + 1

\int \frac{4 x ^{2} + 2}{1 + x ^{2}} d x

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

What is the derivative of y=14^{-8/x} ?
The derivative of y=14^{-8/x} is (ln(14)*2^{(3x-8)/x}*7^{-8/x})/(x^2)
What is the first derivative of y=14^{-8/x} ?
The first derivative of y=14^{-8/x} is (ln(14)*2^{(3x-8)/x}*7^{-8/x})/(x^2)