Find ds/dt s=5t^3-3t^5

Problem

d(s())/d(t)* where *s=5*t3−3*t5

Solution

1. Identify the function to be differentiated with respect to t which is s=5*t3−3*t5

2. Apply the power rule to the first term, 5*t3 by multiplying the coefficient by the exponent and decreasing the exponent by one.

(d(5)*t3)/d(t)=15*t2

3. Apply the power rule to the second term, −3*t5 in the same manner.

(d(−)*3*t5)/d(t)=−15*t4

4. Combine the results to find the derivative of the entire expression.

d(s())/d(t)=15*t2−15*t4

Final Answer

d(s())/d(t)=15*t2−15*t4

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