Solve sum*3*7/4*119/25

$$\sum \times 3 \times \frac { 7 } { 4 } \times \frac { 119 } { 25 }$$

Evaluate

$$\frac{2499Σ}{100}$$

Solution Steps

Express 3\times \frac{7}{4} as a single fraction.

$$Σ\times \frac{3\times 7}{4}\times \frac{119}{25}$$

Multiply 3 and 7 to get 21.

$$Σ\times \frac{21}{4}\times \frac{119}{25}$$

Multiply \frac{21}{4} times \frac{119}{25} by multiplying numerator times numerator and denominator times denominator.

$$Σ\times \frac{21\times 119}{4\times 25}$$

Do the multiplications in the fraction \frac{21\times 119}{4\times 25}.

$$Σ\times \frac{2499}{100}$$

Differentiate w.r.t. Σ

$$\frac{2499}{100} = 24\frac{99}{100} = 24.99$$

Steps Using Definition of a Derivative

Express 3\times \frac{7}{4} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}Σ}(Σ\times \frac{3\times 7}{4}\times \frac{119}{25})$$

Multiply 3 and 7 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}Σ}(Σ\times \frac{21}{4}\times \frac{119}{25})$$

Multiply \frac{21}{4} times \frac{119}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}Σ}(Σ\times \frac{21\times 119}{4\times 25})$$

Do the multiplications in the fraction \frac{21\times 119}{4\times 25}.

$$\frac{\mathrm{d}}{\mathrm{d}Σ}(Σ\times \frac{2499}{100})$$

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

$$\frac{2499}{100}Σ^{1-1}$$

Subtract 1 from 1.

$$\frac{2499}{100}Σ^{0}$$

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

$$\frac{2499}{100}\times 1$$

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

$$\frac{2499}{100}$$