If f ( x ) = sin ⁡ ( π x 3 ) and g ( x ) = 4 x 3 + 2, what is f(g(x))'?

Set up the composite result function.f(g(x))Evaluate&nbsp;f(4x3+2)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(4x3+2)=sin(π(4x3+2)3)Factor&nbsp;2&nbsp;out of&nbsp;4x3+2.f(4x3+2)=sin(π⋅(2(2x3+1))3)Move&nbsp;2&nbsp;to the left of&nbsp;π.f(4x3+2)=sin(2π(2x3+1)3)&nbsp;

Expert answers to "If f ( x ) = sin ⁡..."

College
Calculus and Analysis
Differential Calculus
Derivatives

hisyhauttaq84w

Answered question

2022-05-12

f (x) = \sin (\frac{π x}{3})

and

g (x) = 4 x^{3} + 2

, what is f(g(x))'?

Answer & Explanation

cartonarepcpo4

Beginner2022-05-13Added 12 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (4 x^{3} + 2)$ by substituting in the value of $g$ into $f$ .

$f (4 x^{3} + 2) = \sin (\frac{π (4 x^{3} + 2)}{3})$

Factor $2$ out of $4 x^{3} + 2$ .

$f (4 x^{3} + 2) = \sin (\frac{π \cdot (2 (2 x^{3} + 1))}{3})$

Move $2$ to the left of $π$ .

$f (4 x^{3} + 2) = \sin (\frac{2 π (2 x^{3} + 1)}{3})$

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