Can someone explain step by step on how to find the derivative of 2x√(3x^2 - 5x + 4)?
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Use the chain rule, product rule, and power rules.
d/dx(2x(3x^2 - 5x + 4)^(1/2)) =
2(3x^2 - 5x + 4)^(1/2) + 2x(1/2)(6x - 5)(3x^2- 5x + 4)^(-1/2) =
2(3x^2 - 5x + 4)^(1/2) + (6x^2 - 5x)/(3x^2 - 5x + 4)^(-1/2)
d/dx(2x(3x^2 - 5x + 4)^(1/2)) =
2(3x^2 - 5x + 4)^(1/2) + 2x(1/2)(6x - 5)(3x^2- 5x + 4)^(-1/2) =
2(3x^2 - 5x + 4)^(1/2) + (6x^2 - 5x)/(3x^2 - 5x + 4)^(-1/2)
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im not gonna tell you how, you can figure that out on your own.
but the derivative is 2(sqrt(3x^2 - 5x + 4) + (x)(3(2x)) - 5)/2sqrt(3x^2 - 5x + 4))
but the derivative is 2(sqrt(3x^2 - 5x + 4) + (x)(3(2x)) - 5)/2sqrt(3x^2 - 5x + 4))
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use the formula d/dx(2x√(3x^2 - 5x + 4)
=
12x^2-15x+8/√3x^2-5x+4
=
12x^2-15x+8/√3x^2-5x+4