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# What's h'(x)?

If h(x)=f^2 (x)-g^2 (x), f'(x)=-g(x), and g'(x)=f(x), what's h'(x)?

### 2 Answers by Expert Tutors

Christopher G. | Math Tutor - Algebra, Trig, Calculus, SAT/ACT MathMath Tutor - Algebra, Trig, Calculus, SA...
5.0 5.0 (3 lesson ratings) (3)
1
h(x) = f2(x) - g2(x)
h'(x) = [f2(x) - g2(x)]' = [f2(x)]' - [g2(x)]'

We need to use the chain rule to find [f2(x)]' and [g2(x)]', that is, we need to take the derivative of (something)2, which is 2(something), and then multiply that by the derivative of that something.

[f2(x)]' - [g2(x)]' = 2f(x)f'(x) - 2g(x)g'(x)
= 2f(x)[-g(x)] - 2g(x)[f(x)]
= -2f(x)g(x) - 2f(x)g(x)
= -4f(x)g(x)

Thank you, Christopher. I give you the 'This answers my question!' button.
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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Given :  h( x) = f2(x) - g2 (X) =

f'(X) = g( x)

g' ( x) = f ( X)

Slove for  hâ€˜( x) = ?

h' ( x ) = 2 f(x)(- f â€˜(x)) - 2 g(x) gâ€˜(x) =

= 2 gâ€˜ (x)(- g(x)) - 2 g( x) g'(x) =0
= -4 g' (x) g(x)
or  -4 f(x)g(x)