I'm learning Calculus and I don't know how the solution is wrong, I'm trying the below: $$f(t) = \frac{1}{\sqrt{1 + 5t^{2}}} \ \rightarrow \ (1+5t^2)^\frac{-1}{2} $$ I know I should use a combination of the power and chain rule: $$f'(t) = -\frac{1}{2}(1+5t^2)^\frac{-3}{2} \times 10t$$ This is where I'm stuck
Here is the correct solution, and I don't understand how they got it: $$f'(t) = -\frac{5t}{ (5t^{2} + 1)^\frac{3}{2} } \ $$
UPDATE: They simplified, had a moment there thanks!
Also, you could use the quotient rule: the derivative of the numerator times the denominator minus the numerator times the derivative of the denominator all divided by the denominator squared.
$$f'(t) = \frac{0 - 1\cdot(-\frac{1}{2}(1+5t^2)^{-\frac{1}{2}}\cdot 10t}{1+5t^2} = \frac{-5t}{(1+5t^2)^{\frac{3}{2}}}$$