Solve 10(x^10)(+1/4x^2)

$$10 ( x ^ { 10 } ) ( + \frac { 1 } { 4 } x ^ { 2 } )$$

Evaluate

$$\frac{5x^{12}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

$$10x^{12}\times \frac{1}{4}$$

Multiply 10 and \frac{1}{4} to get \frac{5}{2}.

$$\frac{5}{2}x^{12}$$

Differentiate w.r.t. x

$$30x^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{12}\times \frac{1}{4})$$

Multiply 10 and \frac{1}{4} to get \frac{5}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{2}x^{12})$$

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

$$12\times \frac{5}{2}x^{12-1}$$

Multiply 12 times \frac{5}{2}.

$$30x^{12-1}$$

Subtract 1 from 12.

$$30x^{11}$$