Solve 7x*49x^2

$$7x \times 49 { x }^{ 2 }$$

Evaluate

$$343x^{3}$$

Solution Steps

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

$$7x^{3}\times 49$$

Multiply 7 and 49 to get 343.

$$343x^{3}$$

Differentiate w.r.t. x

$$1029x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}\times 49)$$

Multiply 7 and 49 to get 343.

$$\frac{\mathrm{d}}{\mathrm{d}x}(343x^{3})$$

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

$$3\times 343x^{3-1}$$

Multiply 3 times 343.

$$1029x^{3-1}$$

Subtract 1 from 3.

$$1029x^{2}$$