Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Advertisements
उत्तर
cos (xy) = x
Differentiating with respect to x
`- sin (xy) [x * ("d"y)/("d"x) + y * 1]` = 1
`- x sin (xy) ("d"y)/("d"x) - y sin (xy)` = 1
`- sin (xy) ("d"y)/("d"x) = 1 + y sin (xy)`
`("d"y)/("d"x) = -((1 y sin(xy)))/(x sin (xy))`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = e–mx
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Differentiate the following:
y = `"e"^(xcosx)`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
