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MHTCET 13 Apr 2026 Shift 1 Paper

Question : 123 of 150

Marks: +1, -0

Let

f(x)=x-5

g(x)=[f(4 h(x)+3)]^{2}

h(1)=4, h^{\prime}(1)=-2

g^{\prime}(1)=\ldots

Solution:

Concept:

Differentiate a composite function using the chain rule after simplifying the inner expression.

Explanation:

Given

f(x)=x-5

, first simplify the inner term:

f(4h(x)+3)=(4h(x)+3)-5=4h(x)-2

Therefore,

g(x)=\left(4h(x)-2\right)^2

Differentiate using the chain rule:

g'(x)=2\left(4h(x)-2\right)\cdot 4h'(x)

g'(x)=8h'(x)\left(4h(x)-2\right)

Substitute

h(1)=4

and

h'(1)=-2

g'(1)=8(-2)\left(4(4)-2\right)

g'(1)=-16(16-2)

g'(1)=-16 \times 14 = -224

Answer:

g'(1)=-224

, which is option B.

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