Solve 4/3*3.14*3x*3x*3x

$$\frac{ 4 }{ 3 } \times 3.14 \times 3x \times 3x \times 3x$$

Evaluate

$$\frac{2826x^{3}}{25}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{4}{3}\times 3.14\times 3x^{2}\times 3\times 3x$$

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

$$\frac{4}{3}\times 3.14\times 3x^{3}\times 3\times 3$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}\times \frac{157}{50}\times 3x^{3}\times 3\times 3$$

Multiply \frac{4}{3} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 157}{3\times 50}\times 3x^{3}\times 3\times 3$$

Do the multiplications in the fraction \frac{4\times 157}{3\times 50}.

$$\frac{628}{150}\times 3x^{3}\times 3\times 3$$

Reduce the fraction \frac{628}{150} to lowest terms by extracting and canceling out 2.

$$\frac{314}{75}\times 3x^{3}\times 3\times 3$$

Express \frac{314}{75}\times 3 as a single fraction.

$$\frac{314\times 3}{75}x^{3}\times 3\times 3$$

Multiply 314 and 3 to get 942.

$$\frac{942}{75}x^{3}\times 3\times 3$$

Reduce the fraction \frac{942}{75} to lowest terms by extracting and canceling out 3.

$$\frac{314}{25}x^{3}\times 3\times 3$$

Express \frac{314}{25}\times 3 as a single fraction.

$$\frac{314\times 3}{25}x^{3}\times 3$$

Multiply 314 and 3 to get 942.

$$\frac{942}{25}x^{3}\times 3$$

Express \frac{942}{25}\times 3 as a single fraction.

$$\frac{942\times 3}{25}x^{3}$$

Multiply 942 and 3 to get 2826.

$$\frac{2826}{25}x^{3}$$

Differentiate w.r.t. x

$$\frac{8478x^{2}}{25}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{3}\times 3.14\times 3x^{2}\times 3\times 3x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{3}\times 3.14\times 3x^{3}\times 3\times 3)$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{3}\times \frac{157}{50}\times 3x^{3}\times 3\times 3)$$

Multiply \frac{4}{3} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 157}{3\times 50}\times 3x^{3}\times 3\times 3)$$

Do the multiplications in the fraction \frac{4\times 157}{3\times 50}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{628}{150}\times 3x^{3}\times 3\times 3)$$

Reduce the fraction \frac{628}{150} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{314}{75}\times 3x^{3}\times 3\times 3)$$

Express \frac{314}{75}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{314\times 3}{75}x^{3}\times 3\times 3)$$

Multiply 314 and 3 to get 942.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{942}{75}x^{3}\times 3\times 3)$$

Reduce the fraction \frac{942}{75} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{314}{25}x^{3}\times 3\times 3)$$

Express \frac{314}{25}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{314\times 3}{25}x^{3}\times 3)$$

Multiply 314 and 3 to get 942.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{942}{25}x^{3}\times 3)$$

Express \frac{942}{25}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{942\times 3}{25}x^{3})$$

Multiply 942 and 3 to get 2826.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2826}{25}x^{3})$$

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

$$3\times \frac{2826}{25}x^{3-1}$$

Multiply 3 times \frac{2826}{25}.

$$\frac{8478}{25}x^{3-1}$$

Subtract 1 from 3.

$$\frac{8478}{25}x^{2}$$