Solve -56*3x^8-(4-1)*1/3

$$- 56 \cdot 3 x ^ { 8 - ( 4 - 1 ) } \cdot \frac { 1 } { 3 }$$

Evaluate

$$-56x^{5}$$

Solution Steps

Multiply -56 and 3 to get -168.

$$-168x^{8-\left(4-1\right)}\times \frac{1}{3}$$

Subtract 1 from 4 to get 3.

$$-168x^{8-3}\times \frac{1}{3}$$

Subtract 3 from 8 to get 5.

$$-168x^{5}\times \frac{1}{3}$$

Multiply -168 and \frac{1}{3} to get -56.

$$-56x^{5}$$

Differentiate w.r.t. x

$$-280x^{4}$$

Steps Using Definition of a Derivative

Multiply -56 and 3 to get -168.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-168x^{8-\left(4-1\right)}\times \frac{1}{3})$$

Subtract 1 from 4 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-168x^{8-3}\times \frac{1}{3})$$

Subtract 3 from 8 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-168x^{5}\times \frac{1}{3})$$

Multiply -168 and \frac{1}{3} to get -56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-56x^{5})$$

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

$$5\left(-56\right)x^{5-1}$$

Multiply 5 times -56.

$$-280x^{5-1}$$

Subtract 1 from 5.

$$-280x^{4}$$