# dy/dx=(6x+1)/(√(4x+1)), Calculus

Given that y=x√(4x+1)
Show that dy/dx=(6x+1)/(√(4x+1))

### Comments for dy/dx=(6x+1)/(√(4x+1)), Calculus

 Nov 28, 2011 Derivatives by: Staff Question: Given that y=x√(4x+1) Show that dy/dx=(6x+1)/(√(4x+1)) Answer: Begin by applying the Product Rule (also called Leibniz's Law) to your problem: f(x) = U*V f’(x) = U*V’ + V*U’ Therefore: y = x * √(4x+1) dy/dx = x * dy/dx(√(4x+1)) + (√(4x+1)) * dy/dx(x) Differentiate each part of the expression dy/dx(√(4x+1)) = dy/dx (4x+1)^.5 = 2/[(√(4x+1)] dy/dx(x) = 1 dy/dx = x * dy/dx(√(4x+1)) + (√(4x+1)) * dy/dx(x) = x * 2/[(√(4x+1)] + (√(4x+1)) * 1 = 2x/[(√(4x+1)] + √(4x+1) dy/dx = 2x/[(√(4x+1)] + √(4x+1) Combine the two terms by converting the second term to a fraction, and then adding the first and second terms. Ensure both terms are fractions with a common denominator. This can be accomplished by multiplying the second term by [√(4x+1)]/[√(4x+1)]. dy/dx = 2x/[(√(4x+1)] + [√(4x+1)]*{[√(4x+1)]/[√(4x+1)]} = 2x/[(√(4x+1)] + [√(4x+1)]*{[√(4x+1)]/[√(4x+1)]} = 2x/[(√(4x+1)] + (4x+1)/[√(4x+1)] = [2x + (4x + 1)]/[(√(4x+1)] = [2x + 4x + 1]/[(√(4x+1)] = [6x + 1]/[(√(4x+1)] The final answer is: dy/dx = (6x + 1)/((√(4x+1)) Thanks for writing. Staff www.solving-math-problems.com

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