hw_2.1_basic derivative rules\ndue sunday by 11:59pm points 100.05 submitting an external\nhw_2.1_basic…

hw_2.1_basic derivative rules\ndue sunday by 11:59pm points 100.05 submitting an external\nhw_2.1_basic derivative rules\n11. submit answer practice similar\nattempt 1: 10 attempts remaining.\ndifferentiate (g(t)=-10t^{-3/4}).\nanswer: (g(t)=)

hw_2.1_basic derivative rules\ndue sunday by 11:59pm points 100.05 submitting an external\nhw_2.1_basic derivative rules\n11. submit answer practice similar\nattempt 1: 10 attempts remaining.\ndifferentiate (g(t)=-10t^{-3/4}).\nanswer: (g(t)=)

Answer

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:

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