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.
x3 ex
Differentiate the following with respect to x.
(x2 – 3x + 2) (x + 1)
Differentiate the following with respect to x.
ex sin x
Differentiate the following with respect to x.
ex (x + log x)
If `xsqrt(1 + y) + ysqrt(1 + x)` = 0 and x ≠ y, then prove that `"dy"/"dx" = - 1/(x + 1)^2`
Differentiate sin3x with respect to cos3x.
Differentiate sin2x with respect to x2.
If y = 500e7x + 600e-7x, then show that y2 – 49y = 0.
If y = 2 + log x, then show that xy2 + y1 = 0.
If xy . yx , then prove that `"dy"/"dx" = y/x((x log y - y)/(y log x - x))`
