Solve 5x^2*5x*4x=

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

Evaluate

$$100x^{4}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Multiply 5 and 5 to get 25.

$$25x^{4}\times 4$$

Multiply 25 and 4 to get 100.

$$100x^{4}$$

Differentiate w.r.t. x

$$400x^{3}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{4}\times 4)$$

Multiply 25 and 4 to get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100x^{4})$$

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

$$4\times 100x^{4-1}$$

Multiply 4 times 100.

$$400x^{4-1}$$

Subtract 1 from 4.

$$400x^{3}$$