Calculus Examples

$f (x) = 5 x^{4}$ , $F (x) = a x^{5}$

Step 1

Set up the composite result function.

$f (F (x))$

Step 2

Evaluate $f (a x^{5})$ by substituting in the value of $F$ into $f$ .

$f (a x^{5}) = 5 {(a x^{5})}^{4}$

Step 3

Apply the product rule to $a x^{5}$ .

$f (a x^{5}) = 5 (a^{4} {(x^{5})}^{4})$

Step 4

Multiply the exponents in ${(x^{5})}^{4}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f (a x^{5}) = 5 (a^{4} x^{5 \cdot 4})$

Step 4.2

Multiply $5$ by $4$ .

$f (a x^{5}) = 5 (a^{4} x^{20})$

$f (a x^{5}) = 5 a^{4} x^{20}$