Solve -b^3-3b^3+1+6b^3

$$- b ^ { 3 } - 3 b ^ { 3 } + 1 + 6 b ^ { 3 }$$

Evaluate

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

Solution Steps

Combine -3b^{3} and 6b^{3} to get 3b^{3}.

$$-b^{3}+3b^{3}+1$$

Combine -b^{3} and 3b^{3} to get 2b^{3}.

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

Differentiate w.r.t. b

$$6b^{2}$$

Steps Using Derivative Rule for Sum

Combine -3b^{3} and 6b^{3} to get 3b^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-b^{3}+3b^{3}+1)$$

Combine -b^{3} and 3b^{3} to get 2b^{3}.

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

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}.

$$3\times 2b^{3-1}$$

Multiply 3 times 2.

$$6b^{3-1}$$

Subtract 1 from 3.

$$6b^{2}$$