If f(x5) = 5x3, then f'(x) is equal to from Mathematics Continui

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281.

If f(x5) = 5x3, then f'(x) is equal to

  • 3x25

  • 3x5

  • 3x

  • x5


A.

3x25

Given, fx5 = 5x3Let          x5 = y  x3 = y35         fy = 5y35or          fx = 5x35On differentiating w.r.t. x, we get           f'x = 5 . 35x- 25                  = 3x25


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282.

f(x) = 2a - x   in - a < x < a3x - 2a in a  x

Then, which of the following is true ?

  • f(x) is discontinuous at x = a

  • f(x) is not differentiable at x = a

  • f(x) is differentiable at x   a

  • f(x) is continuous at all x <a


283.

If f(x) = beax + aebx, then f''(0) is equal to

  • 0

  • 2ab

  • ab(a + b)

  • ab


284.

Th function f(x) = log1 +ax - log1 - bxxis not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuousat x = 0 is 

  • a - b

  • a + b

  • log(a) + log(b)

  • 0


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285.

If f(x) = 1 + nx + nn - 12x2 + nn - 1n - 26x3 + ... + xn, then f''(1) is equal to

  • n(n - 1)2n - 1

  • (n - 1)2n - 1

  • n(n - 1)2n - 2

  • n(n - 1)2n


286.

If f(x) = logx2logex, then f'(x) at x = e is

  • 1

  • 1e

  • 12e

  • 0


287.

If f(x) = gx + g- x2 + 2hx + h- x- 1 where g and h are differentiable function, then f'(0)

  • 1

  • 12

  • 32

  • 0


288.

The function f(x) = [x], where [x] denotes the greatest integer not greater than x , is

  • continuous for all non-integral values of x

  • continuous only at positive integral values of x

  • continuous for all real values of x

  • continuous only at rational values of x


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289.

If the three function f(x), g(x) and h(x) are such that h(x) = f(x) g(x) and f'(x) g'(x) = c where c is constant, then

f''xfx + g''xgx + 2cfx . gx is equal to

  • h'(x) . h''(x)

  • hxh''x

  • h''xhx

  • hxh'x


290.

The derivative of eax cos(bx) with respect x is reax cos(bx) tan-1ba when a>0,b>0, then a value of r, is

  • a2 + b2

  • 1ab

  • ab

  • a + b


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