Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
cos3 x
Advertisements
उत्तर
For the following problems chain rule to be used:
`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
`"d"/"dx"` [f(x)]n = n[f(x)]n-1 × `"d"/"dx"`f(x)
y = cos3 x
y = (cos x)3
`"dy"/"dx" = 3(cos x)^(3-1) "d"/"dx" (cos x)`
= 3 cos2 x (-sin x)
= -3 cos2 x sin x
= -3 cos x (sin x cos x) [Multiply and divide by 2]
= `(-3)/2` cos x (2 sin x cos x)
= `(-3)/2` cos x sin 2x
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
`(sqrtx + 1/sqrtx)^2`
Differentiate the following with respect to x.
`(x^2 + x + 1)/(x^2 - x + 1)`
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
If 4x + 3y = log(4x – 3y), then find `"dy"/"dx"`
Differentiate the following with respect to x.
`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
Differentiate sin2x with respect to x2.
Find y2 for the following function:
x = a cosθ, y = a sinθ
If y = 2 + log x, then show that xy2 + y1 = 0.
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
