Solve 6x(7x^4)

$$6x(7 { x }^{ 4 } )$$

Evaluate

$$42x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$6x^{5}\times 7$$

Multiply 6 and 7 to get 42.

$$42x^{5}$$

Differentiate w.r.t. x

$$210x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{5}\times 7)$$

Multiply 6 and 7 to get 42.

$$\frac{\mathrm{d}}{\mathrm{d}x}(42x^{5})$$

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

$$5\times 42x^{5-1}$$

Multiply 5 times 42.

$$210x^{5-1}$$

Subtract 1 from 5.

$$210x^{4}$$