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Hi Paul,

I don't quite know how to approach this question.

Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) =4, g'(2) = 5, and f'(3)=6.

Find r' (1).

Do I need to use any of the derivatives rules?

Many Thanks,

Sam

Questioner:Sam

Country:British Columbia, Canada

Category:Calculus

Private:No

Subject:derivatives

Question:

Hi Paul,

I don't quite know how to approach this question.

Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) =4, g'(2) = 5, and f'(3)=6.

Find r' (1).

Do I need to use any of the derivatives rules?

Many Thanks,

Sam

------------------------------------------------------------

Yes -- the chain rule -- that's what handles composition of functions.

Pretend that x, f, g, h, are variables.

dr/dx = df/dg dg/dh dh/dx

Now let x = 1; dh/dx = h'(1) = 4

Since h(1) = 2, we could get dg/dh at h = 2 = g'(2) = 5 (nice of them to tell us)

Since g(2) = 3, we can get df/dg at g = 2 = f'(3) = 6 (even nicer)

OK, finish up.

Calculus

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All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.**Education/Credentials**

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