\[
\left(\sin(x+y)^{7}\right)'=\left[\sin\left((x+y)^{7}\right)\right]'_{x}=\cos\left((x+y)^{7}\right)\cdot7\cdot(x+y)^{6}\]


vagy \[
\left(\sin^{7}(x+y)\right)'=\left[\left(\sin(x+y)\right)^{7}\right]'_{x}=7\cdot\sin^{6}(x+y)\cdot\cos(x+y)\]