Solve (7x^frac{3{2}})(10.5x^frac{1{2}})

$$( 7 x ^ { \frac { 3 } { 2 } } ) ( 10.5 x ^ { \frac { 1 } { 2 } } )$$

Evaluate

$$\frac{147x^{2}}{2}$$

Solution Steps

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

$$7x^{2}\times 10.5$$

Multiply 7 and 10.5 to get 73.5.

$$73.5x^{2}$$

Differentiate w.r.t. x

$$147x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}\times 10.5)$$

Multiply 7 and 10.5 to get 73.5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(73.5x^{2})$$

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

$$2\times 73.5x^{2-1}$$

Multiply 2 times 73.5.

$$147x^{2-1}$$

Subtract 1 from 2.

$$147x^{1}$$

For any term t, t^{1}=t.

$$147x$$