Q. 54.2( 71 Votes )

# Differentiate the functions given in w.r.t. x.

(x + 3)^{2}. (x + 4)^{3}. (x + 5)^{4}

Answer :

Given: (x + 3)^{2}. (x + 4)^{3}. (x + 5)^{4}

Let y= (x + 3)^{2}. (x + 4)^{3}. (x + 5)^{4}

Taking log on both sides, we get

log y = log((x + 3)^{2}. (x + 4)^{3}. (x + 5)^{4})

⇒log y = log(x + 3)^{2} + log(x + 4)^{3} + log(x + 5)^{4}

⇒log y = 2.log(x + 3) + 3.log(x + 4) + 4.log(x + 5)^{4}

Now, differentiate both sides with respect to x

= (x + 3)(x + 4)^{2}(x + 5)^{3}(9x^{2} + 70x + 133)

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