Calculus Examples

$f (u) = u^{8}$ ; $g (x) = 8 x^{6} + 7$

Step 1

Set up the composite result function.

$g (f (u))$

Step 2

Evaluate $g (u^{8})$ by substituting in the value of $f$ into $g$ .

$g (u^{8}) = 8 {(u^{8})}^{6} + 7$

Step 3

Multiply the exponents in ${(u^{8})}^{6}$ .

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Step 3.1

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

$g (u^{8}) = 8 u^{8 \cdot 6} + 7$

Step 3.2

Multiply $8$ by $6$ .

$g (u^{8}) = 8 u^{48} + 7$