Solve 9/1x^627x^7

$$\frac { 9 } { 1 } x ^ { 6 } 27 x ^ { 7 }$$

Evaluate

$$243x^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 7 to get 13.

$$\frac{9}{1}x^{13}\times 27$$

Anything divided by one gives itself.

$$9x^{13}\times 27$$

Multiply 9 and 27 to get 243.

$$243x^{13}$$

Differentiate w.r.t. x

$$3159x^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 7 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{1}x^{13}\times 27)$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{13}\times 27)$$

Multiply 9 and 27 to get 243.

$$\frac{\mathrm{d}}{\mathrm{d}x}(243x^{13})$$

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

$$13\times 243x^{13-1}$$

Multiply 13 times 243.

$$3159x^{13-1}$$

Subtract 1 from 13.

$$3159x^{12}$$