Solve (7x*5)(89x*69x)

$$(7x \times 5)(89x \times 69x)$$

Evaluate

$$214935x^{3}$$

Solution Steps

Multiply x and x to get x^{2}.

$$7x^{2}\times 5\times 89\times 69x$$

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

$$7x^{3}\times 5\times 89\times 69$$

Multiply 7 and 5 to get 35.

$$35x^{3}\times 89\times 69$$

Multiply 35 and 89 to get 3115.

$$3115x^{3}\times 69$$

Multiply 3115 and 69 to get 214935.

$$214935x^{3}$$

Differentiate w.r.t. x

$$644805x^{2}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}\times 5\times 89\times 69x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}\times 5\times 89\times 69)$$

Multiply 7 and 5 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}x}(35x^{3}\times 89\times 69)$$

Multiply 35 and 89 to get 3115.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3115x^{3}\times 69)$$

Multiply 3115 and 69 to get 214935.

$$\frac{\mathrm{d}}{\mathrm{d}x}(214935x^{3})$$

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

$$3\times 214935x^{3-1}$$

Multiply 3 times 214935.

$$644805x^{3-1}$$

Subtract 1 from 3.

$$644805x^{2}$$