find the derivative of y with respect to x if y = 4(square route of x)(2x+3)
please show work.
please show work.
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Simplify: y = 4 * (2x^(1 + 1/2) + 3x^(1/2))
Simplify: y = 4 * (2x^(3/2) + 3x^(1/2))
Distribute: y = 8x^(3/2) + 12x^(1/2)
Differentiate: dy/dx = (3/2) * 8x^(1/2) + (1/2) * 12x^(-1/2)
Simplify: dy/dx = (24/2)x^(1/2) + (12/2)x^(-1/2)
Simplify: dy/dx = 12x^(1/2) + 6x^(-1/2)
Move negative exponent to denominator: dy/dx = 12x^(1/2) + (6 / x^(1/2))
Common denominator: dy/dx = (12x^(1/2) * x^(1/2) + 6) / x^(1/2)
Simplify: dy/dx = (12x + 6) / x^(1/2)
Factor 6: dy/dx = 6 * (2x + 1) / x^(1/2)
Simplify: y = 4 * (2x^(3/2) + 3x^(1/2))
Distribute: y = 8x^(3/2) + 12x^(1/2)
Differentiate: dy/dx = (3/2) * 8x^(1/2) + (1/2) * 12x^(-1/2)
Simplify: dy/dx = (24/2)x^(1/2) + (12/2)x^(-1/2)
Simplify: dy/dx = 12x^(1/2) + 6x^(-1/2)
Move negative exponent to denominator: dy/dx = 12x^(1/2) + (6 / x^(1/2))
Common denominator: dy/dx = (12x^(1/2) * x^(1/2) + 6) / x^(1/2)
Simplify: dy/dx = (12x + 6) / x^(1/2)
Factor 6: dy/dx = 6 * (2x + 1) / x^(1/2)