Solve -3x^18+(x^3)^6

$$- 3 x ^ { 18 } + ( x ^ { 3 } ) ^ { 6 }$$

Evaluate

$$-2x^{18}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$-3x^{18}+x^{18}$$

Combine -3x^{18} and x^{18} to get -2x^{18}.

$$-2x^{18}$$

Differentiate w.r.t. x

$$-36x^{17}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

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

Combine -3x^{18} and x^{18} to get -2x^{18}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{18})$$

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

$$18\left(-2\right)x^{18-1}$$

Multiply 18 times -2.

$$-36x^{18-1}$$

Subtract 1 from 18.

$$-36x^{17}$$