Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
(ax2 + bx + c)n
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)
Let y = (ax2 + bx + c)n
`"dy"/"dx"= "n"("a"x^2 + "b"x + "c")^("n"-1) "d"/"dx" ("a"x^2 + "b"x + "c")`
= n(ax2 + bx + c)n-1 (2ax + b)
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
3x4 – 2x3 + x + 8
Differentiate the following with respect to x.
`(3 + 2x - x^2)/x`
Differentiate the following with respect to x.
`(x^2 + x + 1)/(x^2 - x + 1)`
Differentiate the following with respect to x.
x sin x
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
If xm . yn = (x + y)m+n, then show that `"dy"/"dx" = y/x`
Differentiate sin3x with respect to cos3x.
If y = 500e7x + 600e-7x, then show that y2 – 49y = 0.
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
If y = 2 sin x + 3 cos x, then show that y2 + y = 0.
