Question

What is the first derivative of r with respect to t (i.e., differentiate r with respect to t)? r = 5/(t2)Note: Use ^ to show exponents in your answer, so for example x2 = x^2. Also, type your equation answer without additional spaces.

Answer 1

Answer:

The first derivative of $r(t) = 5\cdot t^{-2}$ (r(t)=5*t^{-2}) with respect to t is $r'(t) = -10\cdot t^{-3}$ (r'(t) = -10*t^{-3}).

Step-by-step explanation:

Let be $r(t) = \frac{5}{t^{2}}$, which can be rewritten as $r(t) = 5\cdot t^{-2}$. The rule of differentiation for a potential function multiplied by a constant is:

$\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}$, $\forall \,n\neq 0$

Then,

$r'(t) = (-2)\cdot 5\cdot t^{-3}$

$r'(t) = -10\cdot t^{-3}$ (r'(t) = -10*t^{-3})

The first derivative of $r(t) = 5\cdot t^{-2}$ (r(t)=5*t^{-2}) with respect to t is $r'(t) = -10\cdot t^{-3}$ (r'(t) = -10*t^{-3}).