Solve 3x^2*5x

$$3 x ^ { 2 } \times 5 x$$

Evaluate

$$15x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3x^{3}\times 5$$

Multiply 3 and 5 to get 15.

$$15x^{3}$$

Differentiate w.r.t. x

$$45x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{3})$$

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

$$3\times 15x^{3-1}$$

Multiply 3 times 15.

$$45x^{3-1}$$

Subtract 1 from 3.

$$45x^{2}$$