To determine

To find: The derivative of y

Answer

y'=8t3t4+12

Explanation

Formula:

i.

Exponent rule,  ddxxn=nxn-1

ii.

Sum rule,  ddxfx+gx=ddx(fx+ddx(g(x)

iii.

Quotient rule,  ddxfxgx=gx*ddx(fx- fx*ddx(gxgx2

iv.

Constant rule, ddxc= 0

Given:

y=t4-1t4+1

Calculation:

Consider the given function

y=t4-1t4+1

Differentiate with respect to t on both sides

ddty=ddtt4-1t4+1

Applying the quotient rule of differentiation

y'=t4+1*ddtt4-1- t4-1*ddt(t4+1)t4+12

By applying the sum rule of differentiation

y'=t4+1*ddtt4+ddt1-t4-1*ddtt4-ddt1t4+12

Applying the exponent rule of differentiation

y'=t4+1*4t3+0- (t4-1)[4t3-0]t4+12

y'=4t3[t4+1-t4+1]t4+12

y'=8t3t4+12

Conclusion:

y'=8t3t4+12