Statement Compute the derivative of y=3 2x+1y=3^{\,2x+1}y=32x+1. Solution Using ddxag(x)=ag(x) g′(x)lna\dfrac{d}{dx}a^{g(x)}=a^{g(x)}\,g'(x)\ln adxdag(x)=ag(x)g′(x)lna with g(x)=2x+1g(x)=2x+1g(x)=2x+1: y′=3 2x+1⋅2⋅ln3=2ln3⋅3 2x+1.y'=3^{\,2x+1}\cdot 2\cdot\ln 3=2\ln 3\cdot 3^{\,2x+1}.y′=32x+1⋅2⋅ln3=2ln3⋅32x+1.