Solve 9+5s^2-2s^2-8+3s^2

$$9+5 { s }^{ 2 } -2 { s }^{ 2 } -8+3 { s }^{ 2 }$$

Evaluate

$$6s^{2}+1$$

Solution Steps

Combine 5s^{2} and -2s^{2} to get 3s^{2}.

$$9+3s^{2}-8+3s^{2}$$

Subtract 8 from 9 to get 1.

$$1+3s^{2}+3s^{2}$$

Combine 3s^{2} and 3s^{2} to get 6s^{2}.

$$1+6s^{2}$$

Differentiate w.r.t. s

$$12s$$

Steps Using Derivative Rule for Sum

Combine 5s^{2} and -2s^{2} to get 3s^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(9+3s^{2}-8+3s^{2})$$

Subtract 8 from 9 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}s}(1+3s^{2}+3s^{2})$$

Combine 3s^{2} and 3s^{2} to get 6s^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(1+6s^{2})$$

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}.

$$2\times 6s^{2-1}$$

Multiply 2 times 6.

$$12s^{2-1}$$

Subtract 1 from 2.

$$12s^{1}$$

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

$$12s$$