Solve (x^6-5)+(x^6+5)

$$( x ^ { 6 } - 5 ) + ( x ^ { 6 } + 5 )$$

Evaluate

$$2x^{6}$$

Solution Steps

Combine x^{6} and x^{6} to get 2x^{6}.

$$2x^{6}-5+5$$

Add -5 and 5 to get 0.

$$2x^{6}$$

Differentiate w.r.t. x

$$12x^{5}$$

Steps Using Definition of a Derivative

Combine x^{6} and x^{6} to get 2x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}-5+5)$$

Add -5 and 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6})$$

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

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

Multiply 6 times 2.

$$12x^{6-1}$$

Subtract 1 from 6.

$$12x^{5}$$