Solve x^-2y^3*4x^2y^0

$$x ^ { - 2 } y ^ { 3 } \cdot 4 x ^ { 2 } y ^ { 0 }$$

Evaluate

$$4y^{3}$$

Solution Steps

Multiply x^{-2} and x^{2} to get 1.

$$y^{3}\times 4y^{0}$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$y^{3}\times 4$$

Differentiate w.r.t. y

$$12y^{2}$$

Steps Using Definition of a Derivative

Multiply x^{-2} and x^{2} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3}\times 4y^{0})$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3}\times 4)$$

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

$$3\times 4y^{3-1}$$

Multiply 3 times 4.

$$12y^{3-1}$$

Subtract 1 from 3.

$$12y^{2}$$