\[\frac{d}{dx} \sqrt{13{x}^{2}-5{x}^{8}}\]
1
Use Chain Rule on ddx13x2−5x8\frac{d}{dx} \sqrt{13{x}^{2}-5{x}^{8}}. Let u=13x2−5x8u=13{x}^{2}-5{x}^{8}. Since u=u12\sqrt{u}={u}^{\frac{1}{2}}, using the Power Rule, dduu12=12u−12\frac{d}{du} {u}^{\frac{1}{2}}=\frac{1}{2}{u}^{-\frac{1}{2}}
1213x2−5x8(ddx13x2−5x8)\frac{1}{2\sqrt{13{x}^{2}-5{x}^{8}}}(\frac{d}{dx} 13{x}^{2}-5{x}^{8})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
26x−40x7213x2−5x8\frac{26x-40{x}^{7}}{2\sqrt{13{x}^{2}-5{x}^{8}}}

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