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Public Submissions: Chain Rule

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Incorrect Questions (6)

Given y=f(u)y = f(u) and u=g(x)u = g(x), what is the general formula for dydx\frac{dy}{dx} according to the Chain Rule?
Your response: dydx=f′(x)⋅g′(u)\frac{dy}{dx} = f'(x) \cdot g'(u)
Calculate the derivative of h(x)=(3x+1)2h(x) = (3x + 1)^2.
Your response: 6x+16x + 1
If y=sin⁡(x2)y = \sin(x^2), what is dydx\frac{dy}{dx}?
Your response: cos⁡(2x)\cos(2x)
Find the derivative of f(x)=e5xf(x) = e^{5x}.
Your response: 15e5x\frac{1}{5}e^{5x}
Differentiate y=ln⁡(cos⁡x)y = \ln(\cos x).
Your response: 1sin⁡x\frac{1}{\sin x}
If f(x)=1+x2f(x) = \sqrt{1 + x^2}, what is f′(x)f'(x)?
Your response: x1+x2x\sqrt{1+x^2}
1 / 7 (14%) 2/5/2026, 2:33:18 PM

Incorrect Questions (5)

Given y=f(u)y = f(u) and u=g(x)u = g(x), what is the general formula for dydx\frac{dy}{dx} according to the Chain Rule?
Your response: dydx=f′(u)+g′(x)\frac{dy}{dx} = f'(u) + g'(x)
If y=sin⁡(x2)y = \sin(x^2), what is dydx\frac{dy}{dx}?
Your response: cos⁡(2x)\cos(2x)
Differentiate y=ln⁡(cos⁡x)y = \ln(\cos x).
Your response: 1sin⁡x\frac{1}{\sin x}
If f(x)=1+x2f(x) = \sqrt{1 + x^2}, what is f′(x)f'(x)?
Your response: 121+x2\frac{1}{2\sqrt{1 + x^2}}
In the function h(x)=sin⁡(cos⁡(x))h(x) = \sin(\cos(x)), which is the "inner" function?
Your response: sin⁡(x)\sin(x)
2 / 7 (29%) 1/24/2026, 1:08:39 AM

Incorrect Questions (7)

Given y=f(u)y = f(u) and u=g(x)u = g(x), what is the general formula for dydx\frac{dy}{dx} according to the Chain Rule?
Your response: dydx=f′(u)+g′(x)\frac{dy}{dx} = f'(u) + g'(x)
Calculate the derivative of h(x)=(3x+1)2h(x) = (3x + 1)^2.
Your response: 9x2+19x^2 + 1
If y=sin⁡(x2)y = \sin(x^2), what is dydx\frac{dy}{dx}?
Your response: 2xsin⁡(x2)2x \sin(x^2)
Find the derivative of f(x)=e5xf(x) = e^{5x}.
Your response: 5xe5x−15xe^{5x-1}
Differentiate y=ln⁡(cos⁡x)y = \ln(\cos x).
Your response: −sin⁡x-\sin x
If f(x)=1+x2f(x) = \sqrt{1 + x^2}, what is f′(x)f'(x)?
Your response: 2x1+x2\frac{2x}{\sqrt{1 + x^2}}
In the function h(x)=sin⁡(cos⁡(x))h(x) = \sin(\cos(x)), which is the "inner" function?
Your response: xx
0 / 7 (0%) 1/24/2026, 12:57:21 AM

Incorrect Questions (0)

Perfect score! No incorrect answers.
 7 / 7 (100%) 1/24/2026, 12:19:32 AM

Incorrect Questions (5)

Calculate the derivative of h(x)=(3x+1)2h(x) = (3x + 1)^2.
Your response: 6x+16x + 1
If y=sin⁡(x2)y = \sin(x^2), what is dydx\frac{dy}{dx}?
Your response: cos⁡(x2)\cos(x^2)
Differentiate y=ln⁡(cos⁡x)y = \ln(\cos x).
Your response: 1cos⁡x\frac{1}{\cos x}
If f(x)=1+x2f(x) = \sqrt{1 + x^2}, what is f′(x)f'(x)?
Your response: 2x1+x2\frac{2x}{\sqrt{1 + x^2}}
In the function h(x)=sin⁡(cos⁡(x))h(x) = \sin(\cos(x)), which is the "inner" function?
Your response: sin⁡(x)\sin(x)
2 / 7 (29%) 1/24/2026, 12:19:06 AM

Incorrect Questions (7)

Given y=f(u)y = f(u) and u=g(x)u = g(x), what is the general formula for dydx\frac{dy}{dx} according to the Chain Rule?
Your response: dydx=f′(u)+g′(x)\frac{dy}{dx} = f'(u) + g'(x)
Calculate the derivative of h(x)=(3x+1)2h(x) = (3x + 1)^2.
Your response: 9x2+19x^2 + 1
If y=sin⁡(x2)y = \sin(x^2), what is dydx\frac{dy}{dx}?
Your response: cos⁡(2x)\cos(2x)
Find the derivative of f(x)=e5xf(x) = e^{5x}.
Your response: 5xe5x−15xe^{5x-1}
Differentiate y=ln⁡(cos⁡x)y = \ln(\cos x).
Your response: 1sin⁡x\frac{1}{\sin x}
If f(x)=1+x2f(x) = \sqrt{1 + x^2}, what is f′(x)f'(x)?
Your response: x1+x2x\sqrt{1+x^2}
In the function h(x)=sin⁡(cos⁡(x))h(x) = \sin(\cos(x)), which is the "inner" function?
Your response: sin⁡(x)\sin(x)
0 / 7 (0%) 1/23/2026, 11:41:55 PM

Incorrect Questions (0)

Perfect score! No incorrect answers.
 7 / 7 (100%) 1/23/2026, 11:41:37 PM

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