Solve 4x^2*x*5x^3

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

Evaluate

$$20x^{6}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$4x^{6}\times 5$$

Multiply 4 and 5 to get 20.

$$20x^{6}$$

Differentiate w.r.t. x

$$120x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}\times 5x^{3})$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6}\times 5)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x^{6})$$

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

$$6\times 20x^{6-1}$$

Multiply 6 times 20.

$$120x^{6-1}$$

Subtract 1 from 6.

$$120x^{5}$$