The derivative of the function is [tex]\frac{3\left(6x+5\right)\left(3x^2+5x+1\right)^{\frac{1}{2}}}{2}[/tex].
What is Derivative?
The derivative is the instantaneous rate of change of a function with respect to one of its variables.
Given function:
y= (3x²+5x+1)[tex]^{3/2}[/tex]
Differentiating and applying chain rule
= 3/2 * (3x²+5x+1)[tex]^{1/2}[/tex] d/dx (3x²+5x+1)
= 3/2 * (3x²+5x+1)[tex]^{1/2}[/tex] (6x+5)
= [tex]\frac{3\left(6x+5\right)\left(3x^2+5x+1\right)^{\frac{1}{2}}}{2}[/tex]
Hence, the value of derivative is [tex]\frac{3\left(6x+5\right)\left(3x^2+5x+1\right)^{\frac{1}{2}}}{2}[/tex]
Learn more about derivative here:
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