Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/x^2`
Advertisements
Solution
y = `sinx/x^2`
`("d"y)/("d"x) = (x^2(cos x) - sin x(2x))/((x^2))`
= `(x^2 cos x - 2x sin x)/x^4`
= `(x[x cos x - 2 sin x])/x^4`
`("d"y)/("d"x) = (x cos x - 2 sin x)/x^3`
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 = `x/(sin x + cosx)`
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
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 = (x2 + 4x + 6)5
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = sin2(cos kx)
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
xy = yx
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:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
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:
Find the derivative of sin x2 with respect to x2
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:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
