Solve 3x^3*5x^2

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

Evaluate

$$15x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 3 and 5 to get 15.

$$15x^{5}$$

Differentiate w.r.t. x

$$75x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{5})$$

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

$$5\times 15x^{5-1}$$

Multiply 5 times 15.

$$75x^{5-1}$$

Subtract 1 from 5.

$$75x^{4}$$