Solve 10x^4:5x^2

$$10 x ^ { 4 } : 5 x ^ { 2 }$$

Evaluate

$$2x^{6}$$

Solution Steps

Divide 10x^{4} by 5 to get 2x^{4}.

$$2x^{4}x^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$2x^{6}$$

Differentiate w.r.t. x

$$12x^{5}$$

Steps Using Definition of a Derivative

Divide 10x^{4} by 5 to get 2x^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}x^{2})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6})$$

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

$$6\times 2x^{6-1}$$

Multiply 6 times 2.

$$12x^{6-1}$$

Subtract 1 from 6.

$$12x^{5}$$