Differentiate the following. Simplify your answer completly. Write your answer w

BenoguigoliB

BenoguigoliB

Answered question

2021-10-14

Differentiate the following. Simplify your answer completly. Write your answer without negative exponents or rational exponents.
f(x)=(3x4+5x2)(2x3+5x4)
Find the slope of the line tangent to f(x)=tanx at x=π4

Answer & Explanation

cyhuddwyr9

cyhuddwyr9

Skilled2021-10-15Added 90 answers

Differentiation the given function as follows,
f(x)=(3x4+5x2)(2x3+5x4)
f(x)=d(3x4+5x2)dx(2x3+5x4)+d(2x3+5x4)dx(3x4+5x2)
=(12x3+5)(2x3+5x4)+(6x220x5)(3x4+5x2)
Simplify the above differential function and write answer without negative exponents or rational exponents.
f(x)=(12x3+5)(2x3+5x4)+(6x320x5)(3x4+5x2)
=24x6+60x+10x3+25x4+18x6+30x312x260x100x4+40x5
=42x6+40x312x275x4+40x5
The slope of the line tangent to f(x)=tanx at x=π4 is given by,
f(x)=tanx
f(x)=sec2x
f(π4)=sec2(π4)
=(2)2
=2
Thus, slope of line tangent to f(x) is 2.

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