Advertisements
Advertisements
Question
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
Solution
`f(x) = (8)/(3root(3)((2x^2 - 7x - 5)^11`
We rewrite the denominator using exponent notation:
`f(x) = (8)/3(2x^2 - 7x - 5)^(11/3)`
`f(x) = 8/g(x)`
`g(x) = 3(2x^2 - 7x - 5)^(11/3)`
`d/dx(c/g(x)) = -(cxxg' (x))/(g(x))^2`
We use the chain rule to differentiate:
`g(x) = 3(2x^2 - 7x - 5)^(11/3)`
`g'(x) = 3xx11/3(2x^2 - 7x - 5)^(11/3-1)xxd/dx (2x^2-7x - 5)`
`g'(x) = 11(2x^2 - 7x-5)^(8/3)xx(4x-7)`
`f'(x) = - (8xx11(2x^2 - 7x - 5)^(8/3) xx (4x-7))/(3(2x^2 - 7x - 5)^(11/3))^2`
`f'(x) = - (88(4x-7)(2x^2-7x-5)^(8/3))/(9(2x^2 - 7x + 5)^(22/3))`
`f'(x) = -(39.11x - 68.44)/(-2x^2 + 7x + 5)^(11/3)`
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t.x: `5^(sin^3x + 3)`
Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`
Differentiate the following w.r.t.x: `e^(3sin^2x - 2cos^2x)`
Differentiate the following w.r.t.x: sec[tan (x4 + 4)]
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x: `log_(e^2) (log x)`
Differentiate the following w.r.t.x: `x/(sqrt(7 - 3x)`
Differentiate the following w.r.t.x: `cot(logx/2) - log(cotx/2)`
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Differentiate the following w.r.t. x : `"cosec"^-1((1)/(4cos^3 2x - 3cos2x))`
Differentiate the following w.r.t. x : `cot^-1((sin3x)/(1 + cos3x))`
Differentiate the following w.r.t. x :
`cos^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `sin^-1(2xsqrt(1 - x^2))`
Differentiate the following w.r.t. x:
`tan^-1((2x^(5/2))/(1 - x^5))`
Differentiate the following w.r.t. x : `tan^-1((2sqrt(x))/(1 + 3x))`
Differentiate the following w.r.t. x :
`tan^(−1)[(2^(x + 2))/(1 − 3(4^x))]`
Differentiate the following w.r.t. x : `cot^-1((a^2 - 6x^2)/(5ax))`
Differentiate the following w.r.t. x :
`tan^-1((5 -x)/(6x^2 - 5x - 3))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x : `((x^2 + 2x + 2)^(3/2))/((sqrt(x) + 3)^3(cosx)^x`
Differentiate the following w.r.t. x : `(x^5.tan^3 4x)/(sin^2 3x)`
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
Differentiate the following w.r.t. x : (sin xx)
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Differentiate the following w.r.t. x :
etanx + (logx)tanx
Differentiate the following w.r.t. x :
(sin x)tanx + (cos x)cotx
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : x7.y5 = (x + y)12
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants: `log((x^20 - y^20)/(x^20 + y^20))` = 20
If f(x) is odd and differentiable, then f′(x) is
If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`
If f(x) = 3x - 2 and g(x) = x2, then (fog)(x) = ________.
If x = `sqrt("a"^(sin^-1 "t")), "y" = sqrt("a"^(cos^-1 "t")), "then" "dy"/"dx"` = ______
Derivative of (tanx)4 is ______
y = {x(x - 3)}2 increases for all values of x lying in the interval.
If f(x) = `(3x + 1)/(5x - 4)` and t = `(5 + 3x)/(x - 4)`, then f(t) is ______
If x = p sin θ, y = q cos θ, then `dy/dx` = ______
