For me personally, the easiest way to do this is by isolating the x² term, and finding the square root of both sides. The hardest way (well actually, the longest way) would be to use the quadratic formula. It just complicates things unnecessarily.
The solution to the above factorization problem is given as f′(x)=4x³−3x²−10x−1. See steps below.
<h3>What are the steps to the above answer?</h3>
Step 1 - Take the derivative of both sides
f′(x)=d/dx(x^4−x^3−5x^2−x−6)
Step 2 - Use differentiation rule d/dx(f(x)±g(x))=d/dx(f(x))±d/dx(g(x))
f′(x)=d/dx(x4)−d/dx(x^3)−d/dx(5x^2)−d/dx(x)−d/dx(6)
f′(x)=4x^3−d/dx(x3)−d/dx(5x^2)−d/dx(x)−d/dx(6)
f′(x)=4x^3−3x2−d/dx(5x^2)−d/dx(x)−d/dx(6)
f′(x)=4x^3−3x^2−10x−d/dx(x)−d/dx(6)
f′(x)=4x^3−3x^2−10x−1−dxd(6)
f′(x)=4x^3−3x^2−10x−1−0
Learn more about factorization:
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Answer:

Step-by-step explanation:

DE :
If y is a solution of given DE then it satisfied the DE.
Differentiate w.r.t t

Using the formula

LHS:
RHS

By using the formula

LHS=RHs
Hence, y is a solution of given DE

Hi,
Work:
Equation;

Write all numerators above the least common denominator 32.

Calculate the sum of positive numbers.

Simplify (FRACTION RESULT)

Or (DECIMAL RESULT)

Hope this helps.
r3t40