Question

Differentiate gt = h-vt-a/ 2t², where h,v and a are constants.

Answer 1

To differentiate the expression gt = h - vt - a/2t², where h, v, and a are constants, we can use the power rule of differentiation. The derivative of gt = h - vt - a/2t² is -v + a/t³, which can also be written as a/t³ - v.

Step-by-step explanation:

To differentiate the expression gt = h - vt - a/2t², where h, v, and a are constants, we can use the power rule of differentiation. The power rule states that if we have an expression of the form ax^n, the derivative is given by d(ax^n)/dx = nax^(n-1). Applying this rule to our expression, we obtain:

First, differentiate h, -vt, and a/2t² separately:

• The derivative of h with respect to t is 0, since h is a constant.
• The derivative of -vt with respect to t is -v, since the derivative of -vt is -v times the derivative of t (which is 1).
• The derivative of a/2t² with respect to t is -a/t³, using the power rule.

Combining these results, the derivative of gt = h - vt - a/2t² is:

0 - v - (-a/t³) = -v + a/t³, which can also be written as a/t³ - v.