Solve x^4*5x^3*x^7

$$x ^ { 4 } \cdot 5 x ^ { 3 } \cdot x ^ { 7 }$$

Evaluate

$$5x^{14}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$x^{14}\times 5$$

Differentiate w.r.t. x

$$70x^{13}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{14}\times 5)$$

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

$$14\times 5x^{14-1}$$

Multiply 14 times 5.

$$70x^{14-1}$$

Subtract 1 from 14.

$$70x^{13}$$