Solve 1/4*3,14*48^2x

$$\frac { 1 } { 4 } \times 3,14 \times 48 ^ { 2 } x$$

Evaluate

$$\frac{45216x}{25}$$

Solution Steps

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.

$$\frac{1}{4}\times \frac{157}{50}\times 48^{2}x$$

Multiply \frac{1}{4} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 157}{4\times 50}\times 48^{2}x$$

Do the multiplications in the fraction \frac{1\times 157}{4\times 50}.

$$\frac{157}{200}\times 48^{2}x$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{157}{200}\times 2304x$$

Express \frac{157}{200}\times 2304 as a single fraction.

$$\frac{157\times 2304}{200}x$$

Multiply 157 and 2304 to get 361728.

$$\frac{361728}{200}x$$

Reduce the fraction \frac{361728}{200} to lowest terms by extracting and canceling out 8.

$$\frac{45216}{25}x$$

Differentiate w.r.t. x

$$1808,64$$

Steps Using Definition of a Derivative

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.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}\times \frac{157}{50}\times 48^{2}x)$$

Multiply \frac{1}{4} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\times 157}{4\times 50}\times 48^{2}x)$$

Do the multiplications in the fraction \frac{1\times 157}{4\times 50}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{157}{200}\times 48^{2}x)$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{157}{200}\times 2304x)$$

Express \frac{157}{200}\times 2304 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{157\times 2304}{200}x)$$

Multiply 157 and 2304 to get 361728.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{361728}{200}x)$$

Reduce the fraction \frac{361728}{200} to lowest terms by extracting and canceling out 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{45216}{25}x)$$

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

$$\frac{45216}{25}x^{1-1}$$

Subtract 1 from 1.

$$\frac{45216}{25}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{45216}{25}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{45216}{25}$$