Solve 12x^3:3x^8=

$$12 x ^ { 3 } : 3 x ^ { 8 } =$$

Evaluate

$$4x^{11}$$

Solution Steps

Divide 12x^{3} by 3 to get 4x^{3}.

$$4x^{3}x^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$4x^{11}$$

Differentiate w.r.t. x

$$44x^{10}$$

Steps Using Definition of a Derivative

Divide 12x^{3} by 3 to get 4x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}x^{8})$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{11})$$

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

$$11\times 4x^{11-1}$$

Multiply 11 times 4.

$$44x^{11-1}$$

Subtract 1 from 11.

$$44x^{10}$$