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:
f(x) = x sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/x^2`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Differentiate the following:
y = tan 3x
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
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^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
If y = sin–1x then find y”
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Find the derivatives of the following:
If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
