Solve 8b^3+18b^2+4b^2-5

$$8 b ^ { 3 } + 18 b ^ { 2 } + 4 b ^ { 2 } - 5$$

Differentiate w.r.t. b

$$4b\left(6b+11\right)$$

Steps Using Derivative Rule for Sum

Combine 18b^{2} and 4b^{2} to get 22b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(8b^{3}+22b^{2}-5)$$

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}.

$$3\times 8b^{3-1}+2\times 22b^{2-1}$$

Multiply 3 times 8.

$$24b^{3-1}+2\times 22b^{2-1}$$

Subtract 1 from 3.

$$24b^{2}+2\times 22b^{2-1}$$

Multiply 2 times 22.

$$24b^{2}+44b^{2-1}$$

Subtract 1 from 2.

$$24b^{2}+44b^{1}$$

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

$$24b^{2}+44b$$

Evaluate

$$8b^{3}+22b^{2}-5$$

Solution Steps

Combine 18b^{2} and 4b^{2} to get 22b^{2}.

$$8b^{3}+22b^{2}-5$$