Solve 12x^9div3x^6)*2x^2

$$12 x ^ { 9 } \div 3 x ^ { 6 } ) \times 2 x ^ { 2 }$$

Evaluate

$$4x^{15}$$

Solution Steps

Divide 12x^{9} by 3 to get 4x^{9}.

$$4x^{9}x^{6}$$

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$4x^{15}$$

Differentiate w.r.t. x

$$60x^{14}$$

Steps Using Definition of a Derivative

Divide 12x^{9} by 3 to get 4x^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{9}x^{6})$$

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{15})$$

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

$$15\times 4x^{15-1}$$

Multiply 15 times 4.

$$60x^{15-1}$$

Subtract 1 from 15.

$$60x^{14}$$