Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos x
Advertisements
Solution
y = x sin x cos x
y = `1/2* 2 sin x cos x`
y = `1/2 x * sin 2x`
`("d"y)/("d"x) = 1/2 [x cos 2x xx 2 + sin 2x xx 1]`
`("d"y)/("d"x) = 1/2 [2x cos 2x + 2 sin x cos x]`
= `1/2 xx 2[x cos 2x + sin x cos x]`
`("d"y)/("d"x) = x cos 2x + sin x cos x`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x + cos x
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 = ex sin x
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 = sin x0
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = sin (ex)
Differentiate the following:
y = e–mx
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
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 y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
If f(x) = `{{:(x - 5, "if" x ≤ 1),(4x^2 - 9, "if" 1 < x < 2),(3x + 4, "if" x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is
