What is the derivative of (,\at)/(Bt^2+Ct^3) ?

The derivative of (,\at)/(Bt^2+Ct^3) is (,\at)(-1/((Bt^2+Ct^3)^2)t^2)

What is the first derivative of (,\at)/(Bt^2+Ct^3) ?

The first derivative of (,\at)/(Bt^2+Ct^3) is (,\at)(-1/((Bt^2+Ct^3)^2)t^2)

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derivative of

\frac{, at}{B t ^{2} + C t ^{3}}

(, at) (- \frac{1}{( B t ^{2} + C t ^{3} ) ^{2}} t^{2})

Solution steps

\frac{d}{d B} (\frac{, at}{B t ^{2} + C t ^{3}})

Treat

t, C

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= (, at) \frac{d}{d B} (\frac{1}{B t ^{2} + C t ^{3}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= (, at) \frac{d}{d B} ((B t^{2} + C t^{3})^{- 1})

Apply the chain rule:

- \frac{1}{( B t ^{2} + C t ^{3} ) ^{2}} \frac{d}{d B} (B t^{2} + C t^{3})

= - \frac{1}{( B t ^{2} + C t ^{3} ) ^{2}} \frac{d}{d B} (B t^{2} + C t^{3})

\frac{d}{d B} (B t^{2} + C t^{3}) = t^{2}

= (, at) (- \frac{1}{( B t ^{2} + C t ^{3} ) ^{2}} t^{2})

What is the derivative of (,\at)/(Bt^2+Ct^3) ?
The derivative of (,\at)/(Bt^2+Ct^3) is (,\at)(-1/((Bt^2+Ct^3)^2)t^2)
What is the first derivative of (,\at)/(Bt^2+Ct^3) ?
The first derivative of (,\at)/(Bt^2+Ct^3) is (,\at)(-1/((Bt^2+Ct^3)^2)t^2)