Solve 49/25B^4*(-5/49A)-5/12AB^4*(-3/10)=

$$\frac { 49 } { 25 } B ^ { 4 } \cdot ( - \frac { 5 } { 49 } A ) - \frac { 5 } { 12 } A B ^ { 4 } \cdot ( - \frac { 3 } { 10 } ) =$$

Evaluate

$$-\frac{3AB^{4}}{40}$$

Solution Steps

Multiply \frac{49}{25} and -\frac{5}{49} to get -\frac{1}{5}.

$$-\frac{1}{5}B^{4}A-\frac{5}{12}AB^{4}\left(-\frac{3}{10}\right)$$

Multiply \frac{5}{12} and -\frac{3}{10} to get -\frac{1}{8}.

$$-\frac{1}{5}B^{4}A-\left(-\frac{1}{8}AB^{4}\right)$$

The opposite of -\frac{1}{8}AB^{4} is \frac{1}{8}AB^{4}.

$$-\frac{1}{5}B^{4}A+\frac{1}{8}AB^{4}$$

Combine -\frac{1}{5}B^{4}A and \frac{1}{8}AB^{4} to get -\frac{3}{40}B^{4}A.

$$-\frac{3}{40}B^{4}A$$

Differentiate w.r.t. B

$$-\frac{3AB^{3}}{10}$$