Solve 4x/5b*25b^2x^3/2x

$$\frac { 4 x } { 5 b } \cdot \frac { 25 b ^ { 2 } x ^ { 3 } } { 2 x }$$

Evaluate

$$10bx^{3}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{4x}{5b}\times \frac{25b^{2}x^{2}}{2}$$

Multiply \frac{4x}{5b} times \frac{25b^{2}x^{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x\times 25b^{2}x^{2}}{5b\times 2}$$

Cancel out 2\times 5b in both numerator and denominator.

$$2\times 5bxx^{2}$$

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

$$2\times 5bx^{3}$$

Multiply 2 and 5 to get 10.

$$10bx^{3}$$

Differentiate w.r.t. x

$$30bx^{2}$$