Solve 6x^4:2x^3

$$6 x ^ { 4 } : 2 x ^ { 3 }$$

Evaluate

$$3x^{7}$$

Solution Steps

Divide 6x^{4} by 2 to get 3x^{4}.

$$3x^{4}x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$3x^{7}$$

Differentiate w.r.t. x

$$21x^{6}$$

Steps Using Definition of a Derivative

Divide 6x^{4} by 2 to get 3x^{4}.

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

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

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

$$7\times 3x^{7-1}$$

Multiply 7 times 3.

$$21x^{7-1}$$

Subtract 1 from 7.

$$21x^{6}$$