Question

Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate y=(6x²+7)(6x+5+x³)

a. Apply the Product Rule Let u=(6x²+7) and v=(6x+5+x³) dxd(uv)=(6x²+7)(□)+(6x+5+x³)
b. Multiply the factors of the original expression, u and v, to produce a sum of simpler terms y= (Simplify your answer) Find y' y′=

Answer 1

To find y', you can apply the Product Rule by letting u = 6x² + 7 and v = 6x + 5 + x³. Then, differentiate u and v to get du/dx and dv/dx. Substitute these values into the Product Rule formula y' = u(dv/dx) + v(du/dx).

Step-by-step explanation:

To find y' using the Product Rule, we can let u = 6x² + 7 and v = 6x + 5 + x³. Then, we differentiate u and v with respect to x to get du/dx and dv/dx, and apply the Product Rule formula: y' = u(dv/dx) + v(du/dx).

(a) Applying the Product Rule: Let u=(6x²+7) and v=(6x+5+x³). dxd(uv)=(6x²+7)(6)+(6x+5+x³)(12x²+6).

(b) Multiplying the factors of the original expression, u and v, to produce a sum of simpler terms: y = (6x² + 7)(6x + 5 + x³) = 36x³ + 30x² + 6x² + 42x + 7x³ + 35 + x⁶.

Finally, y' can be found by simplifying the terms and combining like terms if necessary.