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

Problem

d()/d(t)*(2*t2+√(,t3))

Solution

1. Rewrite the expression using rational exponents to make it easier to differentiate.

√(,t3)=t(3/2)

2. Apply the sum rule for derivatives, which allows for differentiating each term separately.

d()/d(t)*(2*t2+t(3/2))=(d(2)*t2)/d(t)+d(t(3/2))/d(t)

3. Apply the power rule, d(tn)/d(t)=n*t(n−1) to the first term.

(d(2)*t2)/d(t)=2*(2)*t(2−1)=4*t

4. Apply the power rule to the second term.

d(t(3/2))/d(t)=3/2*t(3/2−1)=3/2*t(1/2)

5. Simplify the expression by combining the results and converting the rational exponent back to radical form.

3/2*t(1/2)=(3√(,t))/2

Final Answer

d()/d(t)*(2*t2+√(,t3))=4*t+(3√(,t))/2

Want more problems? Check here!