Differentiation quiz

If y = x^2 + 3x + 2 dy/dx= [blank_start]2[blank_end]x + [blank_start]3[blank_end]

If asked to differentiate y= (x+3)^2, I would use the [blank_start]chain[blank_end] rule

If asked to differentiate y= (x+1)/(x^2 - 2), I would use the [blank_start]quotient[blank_end] rule

The gradient of a tangent is 1/3. The gradient of its normal is [blank_start]-3[blank_end]

If f(x) = X^2 + 2x + 1, the value of x, dy/dx = [blank_start]2[blank_end]x+[blank_start]2[blank_end]. This means the gradient of the curve is 0 when x = [blank_start]-1[blank_end]

y = ln(3x^2) y= ln[blank_start]3[blank_end] + [blank_start]2[blank_end]lnx dy/dx = [blank_start]2/x[blank_end]

y = sin 3x dy/dx = [blank_start]3[blank_end][blank_start]cos[blank_end][blank_start]3x[blank_end]

f(x) = tan2x f'(x) = [blank_start]2[blank_end]sec^2([blank_start]2x[blank_end])

f(x) = 3x^2-x^3 f'(x) = 6x-3x^2 Stationary points are at values of x for which f'(x) = 0, (x = 0 or x = [blank_start]2[blank_end]) f''(x) = [blank_start]6[blank_end] - [blank_start]6[blank_end]x When x=0, stationary point is a [blank_start]minimum[blank_end] because at x=0, f''(x) is positive.

The second derivative of a function is also known as dy^2/dx^2