Find the Derivative - d/dt 4t^3- square root of t+2

Problem

d()/d(t)*(4*t3−√(,t)+2)

Solution

1. Rewrite the expression using power notation to make differentiation easier, changing the square root to an exponent of 1/2

d()/d(t)*(4*t3−t(1/2)+2)

2. Apply the sum and difference rule to differentiate each term of the expression individually.

(d(4)*t3)/d(t)−d(t(1/2))/d(t)+d(2)/d(t)

3. Apply the power rule to the first two terms, where d(tn)/d(t)=n*t(n−1) and use the constant rule for the third term.

12*t2−1/2*t(−1/2)+0

4. Simplify the expression by rewriting the negative fractional exponent as a square root in the denominator.

12*t2−1/(2√(,t))

Final Answer

d()/d(t)*(4*t3−√(,t)+2)=12*t2−1/(2√(,t))

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