Solve 31x^3-4x^3-20x^3

$$31 x ^ { 3 } - 4 x ^ { 3 } - 20 x ^ { 3 }$$

Evaluate

$$7x^{3}$$

Solution Steps

Combine 31x^{3} and -4x^{3} to get 27x^{3}.

$$27x^{3}-20x^{3}$$

Combine 27x^{3} and -20x^{3} to get 7x^{3}.

$$7x^{3}$$

Differentiate w.r.t. x

$$21x^{2}$$

Steps Using Definition of a Derivative

Combine 31x^{3} and -4x^{3} to get 27x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x^{3}-20x^{3})$$

Combine 27x^{3} and -20x^{3} to get 7x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$3\times 7x^{3-1}$$

Multiply 3 times 7.

$$21x^{3-1}$$

Subtract 1 from 3.

$$21x^{2}$$