Solve 12x^{5}-x^5-4x^5-2x^5-3x^5=

$$12 x ^ { 5 } - x ^ { 5 } - 4 x ^ { 5 } - 2 x ^ { 5 } - 3 x ^ { 5 } =$$

Evaluate

$$2x^{5}$$

Solution Steps

Combine 12x^{5} and -x^{5} to get 11x^{5}.

$$11x^{5}-4x^{5}-2x^{5}-3x^{5}$$

Combine 11x^{5} and -4x^{5} to get 7x^{5}.

$$7x^{5}-2x^{5}-3x^{5}$$

Combine 7x^{5} and -2x^{5} to get 5x^{5}.

$$5x^{5}-3x^{5}$$

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

$$2x^{5}$$

Differentiate w.r.t. x

$$10x^{4}$$

Steps Using Definition of a Derivative

Combine 12x^{5} and -x^{5} to get 11x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{5}-4x^{5}-2x^{5}-3x^{5})$$

Combine 11x^{5} and -4x^{5} to get 7x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{5}-2x^{5}-3x^{5})$$

Combine 7x^{5} and -2x^{5} to get 5x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{5}-3x^{5})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5})$$

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

$$5\times 2x^{5-1}$$

Multiply 5 times 2.

$$10x^{5-1}$$

Subtract 1 from 5.

$$10x^{4}$$