Solve 5x^7-8x^7-13x^7-(-6x^7)

$$5 x ^ { 7 } - 8 x ^ { 7 } - 13 x ^ { 7 } - ( - 6 x ^ { 7 } )$$

Evaluate

$$-10x^{7}$$

Solution Steps

Combine 5x^{7} and -8x^{7} to get -3x^{7}.

$$-3x^{7}-13x^{7}-\left(-6x^{7}\right)$$

Combine -3x^{7} and -13x^{7} to get -16x^{7}.

$$-16x^{7}-\left(-6x^{7}\right)$$

The opposite of -6x^{7} is 6x^{7}.

$$-16x^{7}+6x^{7}$$

Combine -16x^{7} and 6x^{7} to get -10x^{7}.

$$-10x^{7}$$

Differentiate w.r.t. x

$$-70x^{6}$$

Steps Using Definition of a Derivative

Combine 5x^{7} and -8x^{7} to get -3x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{7}-13x^{7}-\left(-6x^{7}\right))$$

Combine -3x^{7} and -13x^{7} to get -16x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-16x^{7}-\left(-6x^{7}\right))$$

The opposite of -6x^{7} is 6x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-16x^{7}+6x^{7})$$

Combine -16x^{7} and 6x^{7} to get -10x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{7})$$

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

$$7\left(-10\right)x^{7-1}$$

Multiply 7 times -10.

$$-70x^{7-1}$$

Subtract 1 from 7.

$$-70x^{6}$$