____ / 5 \/ x
sqrt(x^5)
Let u=x5u = x^{5}u=x5.
Apply the power rule: u\sqrt{u}u goes to 12u\frac{1}{2 \sqrt{u}}2u1
Then, apply the chain rule. Multiply by ddxx5\frac{d}{d x} x^{5}dxdx5:
Apply the power rule: x5x^{5}x5 goes to 5x45 x^{4}5x4
The result of the chain rule is:
The answer is:
____ / 5 5*\/ x --------- 2*x
____ / 5 15*\/ x ---------- 2 4*x
____ / 5 15*\/ x ---------- 3 8*x