Advertisements
Advertisements
Question
Differentiate the following:
y = sin2(cos kx)
Solution
y = sin2(cos kx)
y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)
`("d"y)/("d"x)` = 2 sin(cos kx) × cos(cos kx) × – sin kx × k × 1
`("d"y)/("d"x)` = sin(2 cos kx) × – k sin kx
`("d"y)/("d"x)` = – k sin kx . sin(2 cos kx)
APPEARS IN
RELATED QUESTIONS
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 = `(tanx - 1)/secx`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
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))`
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
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:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
