Solve xdxdivd(5x^2)

$$x d x \div d ( 5 x ^ { 2 } )$$

Evaluate

$$5x^{4}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{x^{2}d}{d}\times 5x^{2}$$

Cancel out d in both numerator and denominator.

$$x^{2}\times 5x^{2}$$

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

$$x^{4}\times 5$$

Differentiate w.r.t. x

$$20x^{3}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}d}{d}\times 5x^{2})$$

Cancel out d in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\times 5x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 5)$$

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

$$4\times 5x^{4-1}$$

Multiply 4 times 5.

$$20x^{4-1}$$

Subtract 1 from 4.

$$20x^{3}$$