Solve 3x^4*5x^2

$$3 x ^ { 4 } \cdot 5 x ^ { 2 }$$

Evaluate

$$15x^{6}$$

Solution Steps

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

$$3x^{6}\times 5$$

Multiply 3 and 5 to get 15.

$$15x^{6}$$

Differentiate w.r.t. x

$$90x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{6}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{6})$$

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

$$6\times 15x^{6-1}$$

Multiply 6 times 15.

$$90x^{6-1}$$

Subtract 1 from 6.

$$90x^{5}$$