Solve 20x^9div5x^3=

$$20 x ^ { 9 } \div 5 x ^ { 3 } =$$

Evaluate

$$4x^{12}$$

Solution Steps

Divide 20x^{9} by 5 to get 4x^{9}.

$$4x^{9}x^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$4x^{12}$$

Differentiate w.r.t. x

$$48x^{11}$$

Steps Using Definition of a Derivative

Divide 20x^{9} by 5 to get 4x^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{9}x^{3})$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12})$$

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

$$12\times 4x^{12-1}$$

Multiply 12 times 4.

$$48x^{12-1}$$

Subtract 1 from 12.

$$48x^{11}$$