Solve 6^3(1/4b^3)(146^-30)=

$$6 ^ { 3 } ( \frac { 1 } { 4 } b ^ { 3 } ) ( 146 ^ { - 30 } ) =$$

Evaluate

$$\frac{27b^{3}}{42614331294544986450484874601641860282751041969497950901908799488}$$

Solution Steps

Calculate 6 to the power of 3 and get 216.

$$216\times \frac{1}{4}b^{3}\times 146^{-30}$$

Multiply 216 and \frac{1}{4} to get 54.

$$54b^{3}\times 146^{-30}$$

Calculate 146 to the power of -30 and get \frac{1}{85228662589089972900969749203283720565502083938995901803817598976}.

$$54b^{3}\times \frac{1}{85228662589089972900969749203283720565502083938995901803817598976}$$

Multiply 54 and \frac{1}{85228662589089972900969749203283720565502083938995901803817598976} to get \frac{27}{42614331294544986450484874601641860282751041969497950901908799488}.

$$\frac{27}{42614331294544986450484874601641860282751041969497950901908799488}b^{3}$$

Differentiate w.r.t. b

$$\frac{81b^{2}}{42614331294544986450484874601641860282751041969497950901908799488}$$

Steps Using Definition of a Derivative

Calculate 6 to the power of 3 and get 216.

$$\frac{\mathrm{d}}{\mathrm{d}b}(216\times \frac{1}{4}b^{3}\times 146^{-30})$$

Multiply 216 and \frac{1}{4} to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}b}(54b^{3}\times 146^{-30})$$

Calculate 146 to the power of -30 and get \frac{1}{85228662589089972900969749203283720565502083938995901803817598976}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(54b^{3}\times \frac{1}{85228662589089972900969749203283720565502083938995901803817598976})$$

Multiply 54 and \frac{1}{85228662589089972900969749203283720565502083938995901803817598976} to get \frac{27}{42614331294544986450484874601641860282751041969497950901908799488}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{27}{42614331294544986450484874601641860282751041969497950901908799488}b^{3})$$

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

$$3\times \frac{27}{42614331294544986450484874601641860282751041969497950901908799488}b^{3-1}$$

Multiply 3 times \frac{27}{42614331294544986450484874601641860282751041969497950901908799488}.

$$\frac{81}{42614331294544986450484874601641860282751041969497950901908799488}b^{3-1}$$

Subtract 1 from 3.

$$\frac{81}{42614331294544986450484874601641860282751041969497950901908799488}b^{2}$$