Solve 12y^1*42^1*4/128

$$\frac{ 12 { y }^{ 1 \cdot 4 } { 2 }^{ 1 \cdot 4 } }{ 128 }$$

Evaluate

$$\frac{3y^{4}}{2}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{12y^{4}\times 2^{1\times 4}}{128}$$

Multiply 1 and 4 to get 4.

$$\frac{12y^{4}\times 2^{4}}{128}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{12y^{4}\times 16}{128}$$

Multiply 12 and 16 to get 192.

$$\frac{192y^{4}}{128}$$

Divide 192y^{4} by 128 to get \frac{3}{2}y^{4}.

$$\frac{3}{2}y^{4}$$

Differentiate w.r.t. y

$$6y^{3}$$

Steps Using Definition of a Derivative

Multiply 1 and 4 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{12y^{4}\times 2^{1\times 4}}{128})$$

Multiply 1 and 4 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{12y^{4}\times 2^{4}}{128})$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{12y^{4}\times 16}{128})$$

Multiply 12 and 16 to get 192.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{192y^{4}}{128})$$

Divide 192y^{4} by 128 to get \frac{3}{2}y^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3}{2}y^{4})$$

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

$$4\times \frac{3}{2}y^{4-1}$$

Multiply 4 times \frac{3}{2}.

$$6y^{4-1}$$

Subtract 1 from 4.

$$6y^{3}$$