Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
Advertisements
उत्तर
x = a(θ – sin θ) y = a(1 – cos θ)
`"dx"/("d"theta)` = a(1 - cosθ), `"dy"/("d"theta)` = a(0 - (- sin θ)) = a sin θ
`"dy"/"dx" = ("dy"/("d"theta))/("dx"/("d"theta))`
`= ("a" (2sin theta/2 cos theta/2))/(2 sin^2 theta/2)`
`= (cos theta/2)/(sin theta/2)`
`= cot theta/2`
∵ sin θ = 2 sin `theta/2` cos `theta/2`
1 - cos θ = 2 `sin^2 theta/2`
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
`sqrtx + 1/root(3)(x) + e^x`
Differentiate the following with respect to x.
`e^x/(1 + e^x)`
Differentiate the following with respect to x.
(ax2 + bx + c)n
Differentiate the following with respect to x.
`1/sqrt(1 + x^2)`
Find `"dy"/"dx"` for the following function
xy – tan(xy)
Differentiate the following with respect to x.
xsin x
Differentiate the following with respect to x.
(sin x)tan x
Find `"dy"/"dx"` of the following function:
x = ct, y = `c/t`
Find `"dy"/"dx"` of the following function:
x = a cos3θ, y = a sin3θ
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
