Question

hw_2.1_basic derivative rules
due sunday by 11:59pm points 100.05 submitting an external
hw_2.1_basic derivative rules

1. submit answer practice similar

attempt 1: 10 attempts remaining.
differentiate (g(t)=-10t^{-3/4}).
answer: (g(t)=)

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. Here $a=-10$ and $n =-\frac{3}{4}$.

Step2: Calculate the derivative

$g^\prime(t)=-10\times(-\frac{3}{4})t^{-\frac{3}{4}-1}$.
Simplify the coefficient: $-10\times(-\frac{3}{4})=\frac{30}{4}=\frac{15}{2}$.
Simplify the exponent: $-\frac{3}{4}-1=-\frac{3 + 4}{4}=-\frac{7}{4}$.
So $g^\prime(t)=\frac{15}{2}t^{-\frac{7}{4}}$.

Answer:

$\frac{15}{2}t^{-\frac{7}{4}}$