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## onegirl 2 years ago Find an equation of the tangent line to h(x) = f(x)g(x) at x = 1

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1. ingenuus

\[y=[f'(1)g(1) + f(1)g'(1)](x-1) + f(1)g(1)\]

2. campbell_st

well you need the point of the curve which will be (1, h(1)) you need to find the slope... but 1st you need to differentiate the function using the product rule h'(x) = f(x)g'(x) + g(x)f'(x) the slope at x = 1 is found by substituting x = 1 into the 1st derivative(above) h'(1) = f(1)g'(1) + g(1)f'(1) now you have a slope h'(1) and point (1, h(1)) use the point slope formula to find the equation of the tangent.

3. onegirl

ok

4. onegirl

so i got y = g(1)f'(1) + f(1)x g'(1) - f(1) g'(1) + f(1)g(1) is it correct?

5. onegirl

@campell_st ?

6. onegirl

@campbell_st

7. onegirl

@ingenuus did i get it right?

8. ingenuus

no the answer is above

9. onegirl

okay

10. ingenuus

do you understand the equation y=m(x-a) +b ?

11. onegirl

yes

12. ingenuus

what is the slope m in your case

13. onegirl

1?

14. ingenuus

why is it 1?

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