Solve partial/partialt(t+1)^2(t-2)

$$\frac { \partial } { \partial t } ( t + 1 ) ^ { 2 } ( t - 2 )$$

Evaluate

$$3\left(t^{2}-1\right)$$

Steps Using Derivative Rule for Sum

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(t+1\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\left(t^{2}+2t+1\right)\left(t-2\right))$$

Use the distributive property to multiply t^{2}+2t+1 by t-2 and combine like terms.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{3}-3t-2)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3t^{3-1}-3t^{1-1}$$

Subtract 1 from 3.

$$3t^{2}-3t^{1-1}$$

Subtract 1 from 1.

$$3t^{2}-3t^{0}$$

For any term t except 0, t^{0}=1.

$$3t^{2}-3$$

Differentiate w.r.t. t

$$6t$$