Advertisements
Advertisements
Question
Differentiate the following:
y = sin2(cos kx)
Advertisements
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 = cos x – 2 tan x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
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:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = sin (ex)
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = sin3x + cos3x
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
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:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
If y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
