Solve 3x^4*5x^3

$$3 x ^ { 4 } \times 5 x ^ { 3 }$$

Evaluate

$$15x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$3x^{7}\times 5$$

Multiply 3 and 5 to get 15.

$$15x^{7}$$

Differentiate w.r.t. x

$$105x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{7}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{7})$$

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

$$7\times 15x^{7-1}$$

Multiply 7 times 15.

$$105x^{7-1}$$

Subtract 1 from 7.

$$105x^{6}$$