Solve 2x/8*x^3/9=

$$\frac { 2 x } { 8 } \cdot \frac { x ^ { 3 } } { 9 } =$$

Evaluate

$$\frac{x^{4}}{36}$$

Solution Steps

Divide 2x by 8 to get \frac{1}{4}x.

$$\frac{1}{4}x\times \frac{x^{3}}{9}$$

Multiply \frac{1}{4} times \frac{x^{3}}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{3}}{4\times 9}x$$

Multiply 4 and 9 to get 36.

$$\frac{x^{3}}{36}x$$

Express \frac{x^{3}}{36}x as a single fraction.

$$\frac{x^{3}x}{36}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{x^{4}}{36}$$

Differentiate w.r.t. x

$$\frac{x^{3}}{9}$$

Steps Using Definition of a Derivative

Divide 2x by 8 to get \frac{1}{4}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x\times \frac{x^{3}}{9})$$

Multiply \frac{1}{4} times \frac{x^{3}}{9} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 4 and 9 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{36}x)$$

Express \frac{x^{3}}{36}x as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}x}{36})$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{36})$$

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

$$4\times \frac{1}{36}x^{4-1}$$

Multiply 4 times \frac{1}{36}.

$$\frac{1}{9}x^{4-1}$$

Subtract 1 from 4.

$$\frac{1}{9}x^{3}$$