How do you differentiate #sqrtt*(1t^2)#?
For extra fun, you can also use the product rule along with linearity and the power rule:
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate ( \sqrt{t} \cdot (1  t^2) ), you can use the product rule.

Let ( u = \sqrt{t} ) and ( v = 1  t^2 ).

Differentiate ( u ) with respect to ( t ): ( \frac{du}{dt} = \frac{1}{2\sqrt{t}} ).

Differentiate ( v ) with respect to ( t ): ( \frac{dv}{dt} = 2t ).

Apply the product rule: ( \frac{d}{dt} (uv) = u\frac{dv}{dt} + v\frac{du}{dt} ).

Substitute ( u ), ( v ), ( \frac{du}{dt} ), and ( \frac{dv}{dt} ) into the product rule equation.
( \frac{d}{dt} (\sqrt{t} \cdot (1  t^2)) = (\sqrt{t})(2t) + (1  t^2)\frac{1}{2\sqrt{t}} ).

Simplify if necessary.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you differentiate #f(x)=(x^2+1)^3 # using the chain rule?
 How do you differentiate #y=sqrt(2e^x)#?
 How do you use the quotient rule to differentiate #1 / (1 + x²)#?
 How do you differentiate # y= sqrt( (x^2 + 4x + 1)^2+2x)# using the chain rule?
 How do you differentiate #f(x)=lnsqrt(e^(4x)2)# using the chain rule.?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7