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The second derivative is just two derivatives carried out back to back. In this case we just have to differentiate this function once, and then differentiate the result. The derivative of 2e^(2x) can then...

Logarithms, written in the form log_xy, are another type of mathematical 'operation', just like addition or multiplication. Subtraction as the opposite of addition, division is the opposite of m...

solving horizontally, use v=s/t, where s=200, v=25(3)^1/2. Hence t=s/v=8/(3)^1/2 (where t is the time when the ball would reach the fort if it does not reach the ground)Solivng vertica...

∫ xsin3x dx takes the form of any integral ∫ (u)(dv/dx) dx.
∫ (u)(dv/dx) dx = uv - ∫ (v)(du/dx) dx
Taking u=x and dv/dx= sin3x. The equation can be re-written in the form uv - ∫ (v)(du/dx) dx....

(x - 2)² + (y - 2)² = 16 x = 0 --> 4 + (y - 2)² = 16 --> y - 2 = ±2sqrt{2} --> y = 2 ± 2sqrt{2} --> P(0,2 + 2sqrt{2})y = 0 --> (x - 2)² + 4 = 16 ...