Solve TT*2.8^2*7/3

$$T T \cdot 2.8 ^ { 2 } \cdot \frac { 7 } { 3 }$$

Evaluate

$$\frac{1372T^{2}}{75}$$

Solution Steps

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

$$T^{2}\times 2.8^{2}\times \frac{7}{3}$$

Calculate 2.8 to the power of 2 and get 7.84.

$$T^{2}\times 7.84\times \frac{7}{3}$$

Convert decimal number 7.84 to fraction \frac{784}{100}. Reduce the fraction \frac{784}{100} to lowest terms by extracting and canceling out 4.

$$T^{2}\times \frac{196}{25}\times \frac{7}{3}$$

Multiply \frac{196}{25} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$T^{2}\times \frac{196\times 7}{25\times 3}$$

Do the multiplications in the fraction \frac{196\times 7}{25\times 3}.

$$T^{2}\times \frac{1372}{75}$$

Differentiate w.r.t. T

$$\frac{2744T}{75}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}T}(T^{2}\times 2.8^{2}\times \frac{7}{3})$$

Calculate 2.8 to the power of 2 and get 7.84.

$$\frac{\mathrm{d}}{\mathrm{d}T}(T^{2}\times 7.84\times \frac{7}{3})$$

Convert decimal number 7.84 to fraction \frac{784}{100}. Reduce the fraction \frac{784}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}T}(T^{2}\times \frac{196}{25}\times \frac{7}{3})$$

Multiply \frac{196}{25} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}T}(T^{2}\times \frac{196\times 7}{25\times 3})$$

Do the multiplications in the fraction \frac{196\times 7}{25\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}T}(T^{2}\times \frac{1372}{75})$$

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

$$2\times \frac{1372}{75}T^{2-1}$$

Multiply 2 times \frac{1372}{75}.

$$\frac{2744}{75}T^{2-1}$$

Subtract 1 from 2.

$$\frac{2744}{75}T^{1}$$

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

$$\frac{2744}{75}T$$