Solve 18x^7/3x-(x^2)^3

$$\frac { 18 x ^ { 7 } } { 3 x } - ( x ^ { 2 } ) ^ { 3 }$$

Evaluate

$$5x^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{18x^{7}}{3x}-x^{6}$$

Cancel out 3x in both numerator and denominator.

$$6x^{6}-x^{6}$$

Combine 6x^{6} and -x^{6} to get 5x^{6}.

$$5x^{6}$$

Differentiate w.r.t. x

$$30x^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18x^{7}}{3x}-x^{6})$$

Cancel out 3x in both numerator and denominator.

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

Combine 6x^{6} and -x^{6} to get 5x^{6}.

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

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

$$6\times 5x^{6-1}$$

Multiply 6 times 5.

$$30x^{6-1}$$

Subtract 1 from 6.

$$30x^{5}$$