Solve 5x*7x^2

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

Evaluate

$$35x^{3}$$

Solution Steps

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

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

Multiply 5 and 7 to get 35.

$$35x^{3}$$

Differentiate w.r.t. x

$$105x^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 5 and 7 to get 35.

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

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

$$3\times 35x^{3-1}$$

Multiply 3 times 35.

$$105x^{3-1}$$

Subtract 1 from 3.

$$105x^{2}$$