If y=tanx, dy/dx=(secx)^2

Prove that if:

y=tanx,\quad \frac { dy }{ dx } ={ sec }^{ 2 }x

Proof:

sec2x proof

Prove that if:

y=tankx,\quad \frac { dy }{ dx } =k{ sec }^{ 2 }kx

Proof:

y=tankx=tanu\\ \\ \frac { dy }{ du } ={ sec }^{ 2 }u,\\ \\ u=kx,\quad \frac { du }{ dx } =k\\ \\ \frac { du }{ dx } \cdot \frac { dy }{ du } =k{ sec }^{ 2 }kx\\ \\ \therefore \quad \frac { dy }{ dx } =k{ sec }^{ 2 }kx

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