` Wiskundeleraar

## uitwerkingen van de opgaven

Opgave 1

Differentieer:

\eqalign{ & f(x) = x^2 + 4x + 3 \cr & g(x) = 4x^9 - x \cr & h(x) = (3x - 2)^2 \cr & k(x) = \left( {x^2 - 1} \right)\left( {x^2 + 1} \right) \cr}

Opgave 2

Bepaal de afgeleide:

\eqalign{ & f(x) = 5x^2 + 4t \cr & g(t) = 5x^2 + 4t \cr & h(z) = 5x^2 + 4t \cr}

Opgave 3

Differentieer:

\eqalign{ & f(x) = ax^2 + bx + c \cr & g(x) = (x - 1)^3 \cr & h(x) = 2x\left( {x - 1} \right)^3 - x^2 \left( {x - 1} \right)^2 \cr}

Opgave 1

\eqalign{ & f(x) = x^2 + 4x + 3 \cr & f'(x) = 2x + 4 \cr & g(x) = 4x^9 - x \cr & g'(x) = 36x^8 - 1 \cr & h(x) = (3x - 2)^2 \cr & h(x) = 9x^2 - 12x + 4 \cr & h'(x) = 18x - 12 \cr & k(x) = \left( {x^2 - 1} \right)\left( {x^2 + 1} \right) \cr & k(x) = x^4 - 1 \cr & k'(x) = 4x^3 \cr}

Opgave 2

\eqalign{ & f(x) = 5x^2 + 4t \cr & f'(x) = 10x \cr & g(t) = 5x^2 + 4t \cr & g'(t) = 4 \cr & h(z) = 5x^2 + 4t \cr & h'(z) = 0 \cr}

Opgave 3

\eqalign{ & f(x) = ax^2 + bx + c \cr & f'(x) = 2ax + b \cr & g(x) = (x - 1)^3 \cr & g(x) = x^3 - 3x^2 + 3x - 1 \cr & g'(x) = 3x^2 - 6x + 3 \cr & h(x) = 2x\left( {x - 1} \right)^3 - x^2 \left( {x - 1} \right)^2 \cr & h(x) = 2x\left( {x^3 - 3x^2 + 3x - 1} \right) - x^2 \left( {x^2 - 2x + 1} \right) \cr & h(x) = 2x^4 - 6x^3 + 6x^2 - 2x - x^4 + 2x^3 - x^2 \cr & h(x) = x^4 - 4x^3 + 5x^2 - 2x \cr & h'(x) = 4x^3 - 12x^2 + 10x - 2 \cr}