Solve -6x(36x^2)

$$- 6 x ( 36 x ^ { 2 } )$$

Evaluate

$$-216x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-6x^{3}\times 36$$

Multiply -6 and 36 to get -216.

$$-216x^{3}$$

Differentiate w.r.t. x

$$-648x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{3}\times 36)$$

Multiply -6 and 36 to get -216.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-216x^{3})$$

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

$$3\left(-216\right)x^{3-1}$$

Multiply 3 times -216.

$$-648x^{3-1}$$

Subtract 1 from 3.

$$-648x^{2}$$