Quiz 3: Derivatives

[WORK OUT ON PAPER] - Find dy/dx: y = tan(cosx) (Hint: chain rule)

sec^2(cosx) * -sinx

[WORK OUT ON PAPER] - Find dy/dx: 5x^2lnx (Hint: product rule)

10x(lnx) + 1/x(5x^2)

[WORK OUT ON PAPER] - Find dy/dx: e^x/sinx (Hint: quotient rule)

sinx(e^x) - cosx(e^x)/(sinx)^2

[Implicit Differentiation] - If y^2 = x, what is dy/dx?

1/2y

[Implicit Differentiation] - dy/dx of xy?

1y + x * dy/dx

DERIVATIVE of sinx

cosx

DERIVATIVE of cosx

-sinx

DERIVATIVE of tanx

sec^2x

f(x) = x^5, f'(x) = ___

5x^4

f(x) = x^-2, f'(x) = ___

-2x^-3

f(x) = √x, f'(x) = ___

1/2x^-1/2

f(x) = 1/x, f'(x) = ___

-1/x^2

y = lnx, y' = ___

1/x

y = e^x, y' = ___

e^x

d/dx[arcsinu] = ___

u'/√1 - u^2

d/dx[arccosu] = ___

-u'/√1 - u^2

d/dx[arctanu] = ___

u'/1 + u^2

y = 100^x, y' = ___

100^xln100

y = logax, y' = ___

1/xlna

[WORK OUT ON PAPER] - y = log3(X^2 + x), y' = ___

1/(x^2 + x)ln3 * (2x + 1)

Find dy/dx - ln√x

1/2x