Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
Advertisements
Solution
y = `(tanx - 1)/secx`
`("d"y)/("d"x) = (secx(sec^2x - 0) - (tan x - )secx tanx)/(sec x)^2`
`("d"y)/("d"x) = (secx[sec^2x - (tan x - 1) tanx])/(sec^2x)`
= `([sec^3x - tan^2xx + tanx])/secx`
= `((1 + tanx))/secx`
= `cos x (1 + sinx/cosx)`
`("d"y)/("d"x)` = cos x + sin x
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x – 3 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos x
Differentiate the following:
y = sin (ex)
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
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:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – 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
Find the derivatives of the following:
If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` 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
