Solve 4x^3*5x^64x/16x^9

$$4 { x }^{ 3 } \times \frac{ 5 { x }^{ 6 } 4x }{ 16 } { x }^{ 9 }$$

Evaluate

$$5x^{19}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$4x^{3}\times \frac{5x^{7}\times 4}{16}x^{9}$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$4x^{12}\times \frac{5x^{7}\times 4}{16}$$

Multiply 5 and 4 to get 20.

$$4x^{12}\times \frac{20x^{7}}{16}$$

Divide 20x^{7} by 16 to get \frac{5}{4}x^{7}.

$$4x^{12}\times \frac{5}{4}x^{7}$$

Multiply 4 and \frac{5}{4} to get 5.

$$5x^{12}x^{7}$$

To multiply powers of the same base, add their exponents. Add 12 and 7 to get 19.

$$5x^{19}$$

Differentiate w.r.t. x

$$95x^{18}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}\times \frac{5x^{7}\times 4}{16}x^{9})$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12}\times \frac{5x^{7}\times 4}{16})$$

Multiply 5 and 4 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12}\times \frac{20x^{7}}{16})$$

Divide 20x^{7} by 16 to get \frac{5}{4}x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12}\times \frac{5}{4}x^{7})$$

Multiply 4 and \frac{5}{4} to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{12}x^{7})$$

To multiply powers of the same base, add their exponents. Add 12 and 7 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{19})$$

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

$$19\times 5x^{19-1}$$

Multiply 19 times 5.

$$95x^{19-1}$$

Subtract 1 from 19.

$$95x^{18}$$