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Differentiate sin3x-3x= f(x)

f'(x)=3cos3x-3differentiating the sin3xchain ruley =sinu u=3xdy/du=cosu du/dx=3dy/du x du/dx = 3cosuu= 3x3cos3x - 3
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Answered by Amy W. • Maths tutor
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Differentiate sin(2x)/x^2 w.r.t. x

Quotient Rule:d(u/v)/dx = (vu' - uv')/(v 2 )u = sin(2x) => u' = 2cos(2x)v = x 2 => v' = 2x=> (2x 2 cos(2x) - 2xsin(2x))/(x 4 )Product Rule:d(uv)/dx = vu' + uv'u = sin(2x) => u' = 2cos(2x)v = 1/x ...
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Answered by Vinh L. • Maths tutor
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Find the first and second derivative of f(x) = 6/x^2 + 2x

We can rewrite the function to eliminate the annoying 1/x^2 expression by knowing this can also be expressed by x^-2.f(x) = 6x^-2 + 2xNow we can differentiate this function term by term, first 6x^-2. We know...
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A function is defined by f(x)=x/(2x-2)^(1/2): (a)Determine the maximum domain of f. (b)Differentiate f. (c)Find the inflection points of the function's graph.

This is a common A-level question tackling functions and differentiation. (a) First, it should be noted that the function f is defined within the field of real numbers and thus the value of 2x-2 in the squar...
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Demonstrate that (2^n)-1 is not a perfect square for any n>2, n ∈ N.

Assumption: If sqrt(2^n- 1) ∈ℕ , it means that there is a k ∈ ℕ such that (2^n-1) = k^2 ⇒ k is odd, so there is m ∈ ℕ such that (2^n-1)=(2m+1)^2 . By solving the equation we get 2^n= 4m^2+4m+2. We divide bot...
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