Question

F

′
(x)=
x
4

x
2
⋅7⋅(3x+5)
6
−(3x+5)
7
⋅2x
​

Answer 1

The expression
`\(F'(x) = (x^4)/(x^2 \cdot 7 \cdot (3x + 5)^6 - (3x + 5)^7 \cdot 2x)\)` when simplified would be
`\[F'(x) = (x^3)/((3x + 5)^6 \cdot (x - 10)).\]`

To solve the expression
`\(F'(x) = (x^4)/(x^2 \cdot 7 \cdot (3x + 5)^6 - (3x + 5)^7 \cdot 2x)\)`, let's simplify the expression step by step.

First, factor out common terms:

`\[F'(x) = (x^4)/((3x + 5)^6 \cdot (x^2 \cdot 7 - (3x + 5) \cdot 2x)).\]`

Now, simplify the denominator:

`\[F'(x) = (x^4)/((3x + 5)^6 \cdot (7x^2 - 6x^2 - 10x)).\]`

Combine like terms:

`\[F'(x) = (x^4)/((3x + 5)^6 \cdot (x^2 - 10x)).\]`

Factor out \(x\) from the denominator:

`\[F'(x) = (x^4)/(x \cdot (3x + 5)^6 \cdot x(x - 10)).\]`

Simplify further:

`\[F'(x) = (x^3)/((3x + 5)^6 \cdot (x - 10)).\]`

This is the simplified form of the given expression F'(x).

The question probable may be:

Simplify the given expression :

`\(F'(x) = (x^4)/(x^2 \cdot 7 \cdot (3x + 5)^6 - (3x + 5)^7 \cdot 2x)\)`