Solve 225x^3div9x

$$225 x ^ { 3 } \div 9 x$$

Evaluate

$$25x^{4}$$

Solution Steps

Divide 225x^{3} by 9 to get 25x^{3}.

$$25x^{3}x$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$25x^{4}$$

Differentiate w.r.t. x

$$100x^{3}$$

Steps Using Definition of a Derivative

Divide 225x^{3} by 9 to get 25x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{3}x)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{4})$$

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

$$4\times 25x^{4-1}$$

Multiply 4 times 25.

$$100x^{4-1}$$

Subtract 1 from 4.

$$100x^{3}$$