Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x: `log[4^(2x)((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)]`
उत्तर
Let y = `log[4^(2x)((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)]`
= `log4^(2x) + log((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)`
= `2xlog4 + (3)/(2)log((x^2 + 5)/(sqrt(2x^3 - 4)))`
= `2xlog4 + (3)/(2)[log(x^2 + 5) - log sqrt((2x^3 - 4))^(1/2)]`
= `2xlog4 + (3)/(2)[log(x^2 + 5) - log sqrt(2x^3 - 4)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[2xlog4 + 3/2log(x^2 + 5) - 3/4log(2x^3 - 4)]`
= `(2log4)"d"/"dx"(x)+ (3)/(2)"d"/"dx"[log(x^2 + 5)] - (3)/(4)"d"/"dx"[log(2x^3 - 4)]`
= `(2log4) xx 1 + 3/2 xx (1)/(x^2 + 5)."d"/"dx"(x^2 + 5) - 3/4 xx (1)/(2x^3 - 4)."d"/"dx"(2x^3 - 4)`
= `2log4 + (3)/(2(x^2 + 5)) xx (2x + 0) - (3)/(4(2x^3 - 4)) xx (2 xx 3x^2 - 0)`
= `2log4 + (3x)/(x^2 + 5) - (9x^2)/(2(2x^3 - 4)`.
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t.x:
`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Differentiate the following w.r.t.x: cos2[log(x2 + 7)]
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 {log(logx)}]2
Differentiate the following w.r.t.x:
`(x^3 - 5)^5/(x^3 + 3)^3`
Differentiate the following w.r.t.x: `(1 + sinx°)/(1 - sinx°)`
Differentiate the following w.r.t.x: `(e^sqrt(x) + 1)/(e^sqrt(x) - 1)`
Differentiate the following w.r.t.x: log[tan3x.sin4x.(x2 + 7)7]
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:
`(x^2 + 2)^4/(sqrt(x^2 + 5)`
Differentiate the following w.r.t. x : cot–1(x3)
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 : `cot^-1[cot(e^(x^2))]`
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 : `cos^-1((3cos3x - 4sin3x)/5)`
Differentiate the following w.r.t. x :
`cos^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x :
`sin^-1(4^(x + 1/2)/(1 + 2^(4x)))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x:
`x^(x^x) + e^(x^x)`
Differentiate the following w.r.t. x : `10^(x^(x)) + x^(x(10)) + x^(10x)`
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sec((x^5 + y^5)/(x^5 - y^5))` = a2
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `cos^-1((7x^4 + 5y^4)/(7x^4 - 5y^4)) = tan^-1a`
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
Differentiate y = etanx w.r. to x
If y = sin−1 (2x), find `("d"y)/(""d"x)`
If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`
If f(x) = 3x - 2 and g(x) = x2, then (fog)(x) = ________.
If the function f(x) = `(log (1 + "ax") - log (1 - "bx))/x, x ≠ 0` is continuous at x = 0 then, f(0) = _____.
If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) ______
Solve `x + y (dy)/(dx) = sec(x^2 + y^2)`
Let f(x) be a polynomial function of the second degree. If f(1) = f(–1) and a1, a2, a3 are in AP, then f’(a1), f’(a2), f’(a3) are in ______.
