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This can be rewritten as x^1/2 + 4x^-1/2+ 4, hence dy/dx = (1/2)x^-1/2 - 2x^-3/2

say (2x-π/6)=qtan²q = sec²q-1so sec²q-1= 11 - sec q sec²q + sec q -12 = 0(sec q -3) (sec q + 4) = 0sec q = 3 or -4because 0<=x<= πso -π/6 <= q <= 11...

e^ln(2x-3) = e¹
2x-3 = e
x = (e+3)/2

Assuming knowledge of solving regular quadratic equations.Treat this as a regular quadratic equation, except it is in terms of sin(x) instead of just x as you might be used to.So using the quadratic equat...

To answer this question you must use implicit differentiation due to there being both x and y terms. Consequently you must differentiate each term individually as you would usually (by multiplying by the ...