Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `5^((-1)/x)`
Advertisements
उत्तर
y = `5^((-1)/x)`
y = `"e"log^(5 - 1/x)`
y = `"e"^(- 1/xlog 5)`
`("d"y)/("d"x) = "e"^(- 1/x log 5) xx "d"/("d"x) (- 1/x log 5)`
= `"e"^(- 1/x log 5) xx - log 5((-1) x^(- 1 - 1))`
= `"e"^(- 1/x log 5) xx (log 5) x^(- 2)`
= `"e"^(log 5 - 1/x) ((log 5))/x^2`
`("d"y)/("d"x) = (5^(-1/x) (log 5))/x^2`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = 4 sec t + tan t
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = e–mx
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Choose the correct alternative:
If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
