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The derivative of y = sin(3x + 5) is 3cos(3x + 5) but only if x is measured in radians.
In this case, you'll need to apply the chain rule, first taking the derivative of the tan function, and multiplying by the derivative of 3x: y = tan(3x) ∴ dy/dx = 3sec2(3x)
Gradient to the curve at any point is the derivative of y = x2 So the gradient is d/dx of x2 = 2x. When x = 2, 2x = 4 so the gradient of the tangent at x = 2 is 4.
y = x^5 + x^3 + x^2 + x y' = 5x^(5 - 1) + 3x^(3 - 1) + 2x^(2 -1) + 1x^(1 - 1) (note x^1 = x and x^0 = 1) y' = 5x^4 + 3x^2 + 2x + 1
If you mean x2-3x+5 then the answer is none because its discriminant is less than zero