Solve a(x) = 5x^5 - 2x^2 + x + 2 - 5x^3 + x^2

Evaluate

a (x) = 5 x^{5} - 2 x^{2} + x + 2 - 5 x^{3} + x^{2}

Simplify

More Steps

a (x) = 5 x^{5} - x^{2} + x + 2 - 5 x^{3}

Take the derivative of both sides

a^{'} (x) = \frac{d}{d x} (5 x^{5} - x^{2} + x + 2 - 5 x^{3})

Use differentiation rule \frac{d}{d x} (f (x) \pm g (x)) = \frac{d}{d x} (f (x)) \pm \frac{d}{d x} (g (x))

a^{'} (x) = \frac{d}{d x} (5 x^{5}) - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (x) + \frac{d}{d x} (2) - \frac{d}{d x} (5 x^{3})

Calculate

More Steps

a^{'} (x) = 25 x^{4} - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (x) + \frac{d}{d x} (2) - \frac{d}{d x} (5 x^{3})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

a^{'} (x) = 25 x^{4} - 2 x + \frac{d}{d x} (x) + \frac{d}{d x} (2) - \frac{d}{d x} (5 x^{3})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

a^{'} (x) = 25 x^{4} - 2 x + 1 + \frac{d}{d x} (2) - \frac{d}{d x} (5 x^{3})

Use \frac{d}{d x} (c) = 0 to find derivative

a^{'} (x) = 25 x^{4} - 2 x + 1 + 0 - \frac{d}{d x} (5 x^{3})

Calculate

More Steps

a^{'} (x) = 25 x^{4} - 2 x + 1 + 0 - 15 x^{2}

Solution

a^{'} (x) = 25 x^{4} - 2 x + 1 - 15 x^{2}

A(x) = 5x^5 2x^2 + x + 2 5x^3 + x^2