Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Advertisements
उत्तर
x = a cost , y = a sin3t
`("d"x)/("d"t) = 3"a"cos^2"t" (- sin"t")`, `("d"y)/("dt") = 3 "a"sin^2"t" (cos "t")`
`(("d"y)/("dt"))/(("d"x)/("dt")) = (3"a" sin^2"t" cos"t")/(- 3"a" cos^2"t" sin"t")`
`("d"y)/("d"x) = - (sin "t")/(cos "t")`
`("d"y)/("d"x)` = – tan t
APPEARS IN
संबंधित प्रश्न
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 = (x2 + 5) log(1 + x) e–3x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = e–mx
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(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:
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
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:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If y = `(1 - x)^2/x^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
