Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
उत्तर
`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
संबंधित प्रश्न
Differentiate the following w.r.t.x:
`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
Differentiate the following w.r.t.x:
`sqrt(x^2 + sqrt(x^2 + 1)`
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Differentiate the following w.r.t.x: `5^(sin^3x + 3)`
Differentiate the following w.r.t.x: `e^(3sin^2x - 2cos^2x)`
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Differentiate the following w.r.t.x: `log_(e^2) (log x)`
Differentiate the following w.r.t.x: (1 + sin2 x)2 (1 + cos2 x)3
Differentiate the following w.r.t.x: `log[(ex^2(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Differentiate the following w.r.t. x : cot–1(4x)
Differentiate the following w.r.t. x : cos–1(1 –x2)
Differentiate the following w.r.t. x : `sin^4[sin^-1(sqrt(x))]`
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Differentiate the following w.r.t. x :
`cos^-1(sqrt(1 - cos(x^2))/2)`
Differentiate the following w.r.t. x : `tan^-1[(1 - tan(x/2))/(1 + tan(x/2))]`
Differentiate the following w.r.t. x : `cot^-1((sin3x)/(1 + cos3x))`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x : `tan^-1((2^x)/(1 + 2^(2x + 1)))`
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^(x^x) + e^(x^x)`
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Differentiate the following w.r.t. x : `[(tanx)^(tanx)]^(tanx) "at" x = pi/(4)`
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
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sin((x^3 - y^3)/(x^3 + y^3))` = a3
If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.
Differentiate y = `sqrt(x^2 + 5)` w.r. to x
If f(x) is odd and differentiable, then f′(x) is
Differentiate sin2 (sin−1(x2)) w.r. to x
Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x
If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) ______
If y = `(3x^2 - 4x + 7.5)^4, "then" dy/dx` is ______
The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t2 + 3 and w = t2 - t + 2, then the rate of change of W with respect to t at t = 1 is ______
Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.
